diff --git "a/20211029_101219/answers-students.wa.untrained" "b/20211029_101219/answers-students.wa.untrained"
new file mode 100644--- /dev/null
+++ "b/20211029_101219/answers-students.wa.untrained"
@@ -0,0 +1,12201 @@
+
+// both bulbs a and c still have a closed path
+// Bulbs A and C are still in closed paths
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+
+
+2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 and the positive terminal are connected.
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// positive battery is seperated by a gap from terminal 2
+// Terminal 2 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+3 4 <==> 7 8 // EQUI // 5 //
+5 6 7 <==> 9 10 11 // EQUI // 5 //
+8 9 10 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// There is no difference between the two terminals.
+// The terminals are in the same state.
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// the switch has to be contained in the same path as the bulb and the battery
+// The switch and the bulb have to be in the same path
+
+
+1 The :
+2 switch :
+3 and :
+4 the :
+5 bulb :
+6 have :
+7 to :
+8 be :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+3 4 5 6 <==> 6 7 8 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// there is a gap in terminal 1
+// Terminals 1 and 2 are in the same electrical state
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 in :
+7 the :
+8 same :
+9 electrical :
+10 state :
+
+
+1 <==> 6 7 8 9 10 // EQUI // 5 //
+2 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// The battery uses the chemical reation to create voltage
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 <==> 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+9 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// a batter uses a chemical reaction to create voltage
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 <==> 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+9 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// the battery alone is in a closed path
+// The battery is contained in a path which does not contain any other components
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 which :
+9 does :
+10 not :
+11 contain :
+12 any :
+13 other :
+14 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Because there is a gap in the circuit.
+// there is a gap in the circuit
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 the :
+7 circuit :
+
+
+2 <==> 1 // EQUI // 5 //
+3 <==> 2 // EQUI // 5 //
+4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and B are not within the same path as bulb C.
+// Bulb C is in a separate path
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+5 6 <==> 3 // EQUI // 5 //
+7 8 9 10 <==> 4 5 6 7 // EQUI // 5 //
+12 13 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// because there was two negative connections
+// Terminals 1 and 2 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 connected :
+
+
+3 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulb a is on a closed path with the battery
+// there is a path containing A and a different path containing B and C
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A :
+7 and :
+8 a :
+9 different :
+10 path :
+11 containing :
+12 B :
+13 and :
+14 C :
+
+
+1 2 <==> 6 // EQUI // 5 //
+3 <==> 2 // EQUI // 5 //
+4 5 6 7 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// the other terminals are connected to the positive terminal.
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 <==> 1 2 3 4 5 // EQUI // 5 //
+4 5 <==> 6 7 // EQUI // 5 //
+6 7 8 9 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The bulb takes away the path.
+// there is an open path
+
+
+1 there :
+2 is :
+3 an :
+4 open :
+5 path :
+
+
+1 2 <==> 1 // EQUI // 5 //
+3 4 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// There is no gap between the positive terminal and terminal 4
+// Terminal 4 and the positive terminal are not separated by the gap
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+2 <==> 7 8 9 // EQUI // 5 //
+3 4 <==> 10 11 12 // EQUI // 5 //
+5 6 7 8 9 10 11 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// Bulb a created a gap
+// If bulb A burns out, neither B nor C is in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 2 <==> 2 3 // EQUI // 5 //
+4 5 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to the positive terminal of the battery
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the bulb is in a closed circuit
+// the battery is in an open path
+
+
+1 the :
+2 battery :
+3 is :
+4 in :
+5 an :
+6 open :
+7 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// The circuit is not closed around the battery.
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+3 4 5 <==> 5 6 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the bulb is not contained in a closed path.
+// The battery is contained in a path which does not contain any other components
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 which :
+9 does :
+10 not :
+11 contain :
+12 any :
+13 other :
+14 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 9 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// There is a gap in the circuit.
+// there is a gap in a circuit
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 a :
+7 circuit :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulb B and bulb C are still on closed paths with the battery.
+// bulbs A and B are still in closed paths with the battery
+
+
+1 bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 5 // EQUI // 5 //
+7 <==> 6 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Bulb A has a closed pathway
+// Bulb A was still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 5 6 <==> 6 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// bulbs a and c are not in the same closed path as bulb b
+// Bulb B is in a separate path
+
+
+1 Bulb :
+2 B :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+1 2 3 4 <==> 1 2 // EQUI // 5 //
+5 6 <==> 3 // EQUI // 5 //
+7 8 9 10 11 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Only one terminal is involved in the circuit.
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+4 5 <==> 5 6 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// there was closed paths between the battery
+// Bulb A was still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 // EQUI // 5 //
+3 4 <==> 6 7 8 9 10 // EQUI // 5 //
+5 6 7 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// the gap separates the positive battery terminal from terminal 2
+// Terminal 2 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 9 10 11 // EQUI // 5 //
+3 <==> 7 8 // EQUI // 5 //
+4 5 6 7 8 9 10 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulb a, bulb b, and bulb c are contained in differentclosed paths.
+// A and C are in different paths with the battery
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 // EQUI // 5 //
+8 9 <==> 4 // EQUI // 5 //
+10 11 12 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// If any bulb is out, it affects the whole system and everything is blocked from the battery.
+// each bulb is in its own path
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+1 <==> 1 2 // EQUI // 5 //
+13 14 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// it is not in the same path.
+// Bulb A is still in a closed path with the battery
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+2 3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// There will be a gap in the path
+// If bulb A burns out, neither B nor C is in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+2 3 <==> 1 // EQUI // 5 //
+4 5 6 7 8 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Bulb B and C are still contained in a path with the battery
+// bulbs B and C are still in closed paths with the battery
+
+
+1 bulbs :
+2 B :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulbs a and c are still contained in a closed path with the battery.
+// Bulbs A and C are still in closed paths with the battery
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Terminal one is not connected to the positive battery terminal
+// Terminal 1 and the positive terminal are not connected
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// bulb A and switch Z are in a closed path
+// Bulb A is still contained in a closed path with the battery and switch Z.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 Z. :
+
+
+1 2 3 4 5 <==> 1 2 // EQUI // 5 //
+6 <==> 3 // EQUI // 5 //
+7 8 9 10 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Terminal 5 is connected to the postitive battery terminal
+// Terminal 5 and the positive terminal are connected
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Terminal 6 is connected to the positive battery terminal
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the red x means that the circuit is not safe.
+// there is a short circuit
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+1 2 3 <==> 1 // EQUI // 5 //
+6 7 <==> 3 4 5 // EQUI // 5 //
+8 9 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// both bulbs B and C are in the same path as bulb A
+// If bulb A burns out, neither B nor C is in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 <==> 6 7 8 9 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+7 8 9 10 <==> 11 12 13 14 // EQUI // 5 //
+12 13 <==> 2 3 // EQUI // 5 //
+
+
+
+
+
+// if the electrical state is non-zero you can find the gap in the circuit
+// A non-zero voltage means that there is a gap
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 there :
+7 is :
+8 a :
+9 gap :
+
+
+2 3 4 <==> 6 // EQUI // 5 //
+5 <==> 7 // EQUI // 5 //
+6 <==> 1 2 3 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+10 11 <==> 8 9 // EQUI // 5 //
+
+
+
+
+
+// The battery is contained in a closed circuit and there is nothing in its pathway
+// The battery is contained in a closed path which does not contain any other components
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 which :
+10 does :
+11 not :
+12 contain :
+13 any :
+14 other :
+15 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+9 <==> 9 // EQUI // 5 //
+12 <==> 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// A terminal is not connected to the positive battery terminal.
+// Terminals 1 and 4 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 5 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// there is a gap in the circuit
+// Terminals 1 and 4 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+1 <==> 1 2 3 4 // EQUI // 5 //
+2 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal is not seperated by a gap from terminal 5
+// Terminal 5 and the positive terminal are not separated by the gap
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 6 <==> 7 8 9 // EQUI // 5 //
+7 8 9 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// You can find where there is a gap
+// Measuring voltage indicates whether two terminals are separated by a gap.
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 whether :
+5 two :
+6 terminals :
+7 are :
+8 separated :
+9 by :
+10 a :
+11 gap. :
+
+
+1 <==> 1 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+6 <==> 7 8 // EQUI // 5 //
+7 8 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// has to do something with a gap
+// Terminal 2 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+4 <==> 7 8 // EQUI // 5 //
+5 6 7 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Because the positive circuit has a voltage of 1.5 volts.
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+2 3 4 <==> 9 10 11 // EQUI // 5 //
+5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// There is a chemical reaction.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+2 <==> 3 // EQUI // 5 //
+3 4 5 <==> 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// when the switch is the in a closed path with the bulb
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 4 5 6 // EQUI // 5 //
+4 <==> 7 8 // EQUI // 5 //
+6 7 8 9 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulb b and c are in a closed path
+// B and C are in the same path
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 <==> 4 // EQUI // 5 //
+6 7 8 9 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// There is a difference in electrical states.
+// the terminals are not connected
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// the bulb will not light
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 2 <==> 1 // EQUI // 5 //
+3 4 5 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// bulb a and c are contained on the same path with the battery
+// A and C are not in the same path with the battery
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 5 // EQUI // 5 //
+7 8 9 10 <==> 6 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The path does not close
+// the battery is in an open path
+
+
+1 the :
+2 battery :
+3 is :
+4 in :
+5 an :
+6 open :
+7 path :
+
+
+1 2 3 4 5 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// The difference between the electrical states is 1.5 volts
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 9 10 11 // EQUI // 5 //
+7 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// there is still a closed path
+// If bulb A burns out, bulbs B and C are still in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 bulbs :
+7 B :
+8 and :
+9 C :
+10 are :
+11 still :
+12 in :
+13 a :
+14 closed :
+15 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 10 // EQUI // 5 //
+3 <==> 11 // EQUI // 5 //
+4 5 6 <==> 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// a gap causes a lost connection
+// A non-zero voltage means that the terminals are not connected.
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 the :
+7 terminals :
+8 are :
+9 not :
+10 connected. :
+
+
+1 2 <==> 1 2 3 // EQUI // 5 //
+3 <==> 4 // EQUI // 5 //
+4 5 6 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal and terminal 6 are connected
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal is connected to terminal 6
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Because there is no gap at terminal 1
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+2 <==> 5 6 7 8 9 // EQUI // 5 //
+3 4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is conncted to the positive terminal
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// When the switch is in the same papth as the bulb.
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+4 <==> 7 8 // EQUI // 5 //
+5 6 7 8 <==> 9 10 11 12 // EQUI // 5 //
+10 11 <==> 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and C are in separate paths.
+// A and C are in different paths
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 <==> 4 // EQUI // 5 //
+6 7 8 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb a and bulb b are still in a closed path with the battery.
+// bulbs A and B are still in closed paths with the battery
+
+
+1 bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 5 // EQUI // 5 //
+7 <==> 6 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The positive battery terminal was not separted by a gap from terminal 6
+// Terminal 6 and the positive terminal are not separated by the gap
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+5 6 7 <==> 7 8 9 // EQUI // 5 //
+8 9 10 <==> 10 11 12 // EQUI // 5 //
+11 12 13 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// A GAP WIL BE CREATED
+// If bulb A burns out, neither B nor C is in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 2 <==> 11 12 13 14 // EQUI // 5 //
+3 4 5 <==> 10 // EQUI // 5 //
+
+
+
+
+
+// bulb a and c are contained in different paths with the battery
+// A and C are in different paths with the battery
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 // EQUI // 5 //
+7 8 9 <==> 5 6 7 // EQUI // 5 //
+10 11 12 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// The positive terminal is connected to terminal 4.
+// Terminal 4 and the positive terminal are connected
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// not contained inthe same path
+// If C burns out, then A and B are still in a closed path.
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+1 2 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulb c does not create a gap in the path for bulb b and a
+// If C is damaged, A and B are still in a closed path
+
+
+1 If :
+2 C :
+3 is :
+4 damaged, :
+5 A :
+6 and :
+7 B :
+8 are :
+9 still :
+10 in :
+11 a :
+12 closed :
+13 path :
+
+
+1 2 <==> 2 // EQUI // 5 //
+3 4 5 <==> 3 // EQUI // 5 //
+6 7 8 9 10 <==> 10 11 12 13 // EQUI // 5 //
+11 12 13 14 15 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// becuase the other terminals are connected to the positive battery terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+5 6 <==> 6 7 // EQUI // 5 //
+7 8 9 10 11 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// because terminal one and the positive battery terminal are on a closed path
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+2 3 4 5 6 7 8 <==> 1 2 // EQUI // 5 //
+9 10 11 12 13 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// Battery will always have voltage.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 // EQUI // 5 //
+4 <==> 7 8 // EQUI // 5 //
+5 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the terminals are not connected
+// Terminal 1 and the positive terminal are not connected
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal is connected to terminal 6
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 4 <==> 1 2 3 4 5 6 // EQUI // 5 //
+5 6 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// bulb a was on a closed path
+// Bulb A is still contained in a closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Because terminal 4 is connected to the negative terminal
+// Terminal 4 and the positive battery terminal are in the same electrical state
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 battery :
+7 terminal :
+8 are :
+9 in :
+10 the :
+11 same :
+12 electrical :
+13 state :
+
+
+2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+4 5 <==> 8 9 10 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// bulb c is in its own pathway
+// Bulb C is in a separate path
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// the voltage is nearest the burnt out bulb
+// Measuring voltage indicates the place where the electrical state changes due to a damaged bulb.
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 damaged :
+15 bulb. :
+
+
+1 2 <==> 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 8 <==> 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// You needed both a battery and a blub with the same path, and the path must be closed
+// there is a closed path containing both the bulb and a battery
+
+
+1 there :
+2 is :
+3 a :
+4 closed :
+5 path :
+6 containing :
+7 both :
+8 the :
+9 bulb :
+10 and :
+11 a :
+12 battery :
+
+
+3 <==> 7 // EQUI // 5 //
+4 5 6 7 8 <==> 8 9 10 11 12 // EQUI // 5 //
+16 17 <==> 2 // EQUI // 5 //
+18 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Because the battery runs in a closed circuit.
+// there is an incomplete circuit
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 3 4 5 // EQUI // 5 //
+4 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// If bulb B is damaged, then the circut is no longer closed.
+// there is no closed path
+
+
+1 there :
+2 is :
+3 no :
+4 closed :
+5 path :
+
+
+1 <==> 1 // EQUI // 5 //
+9 <==> 2 // EQUI // 5 //
+10 11 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// terminal 1, terminal 2, and terminal 3 are connected o the negative battery
+// Terminals 1, 2 and 3 are connected to the negative battery terminal
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 // EQUI // 5 //
+8 9 <==> 6 7 // EQUI // 5 //
+10 11 12 13 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// "Because it didn""t cause a gap."
+// each bulb is in its own path
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 // EQUI // 5 //
+5 6 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// because there is a gap between terminal 1 and terminal 6.
+// There is a gap between terminals 1 and 6
+
+
+1 There :
+2 is :
+3 a :
+4 gap :
+5 between :
+6 terminals :
+7 1 :
+8 and :
+9 6 :
+
+
+3 <==> 2 // EQUI // 5 //
+4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 9 10 11 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// because bulbs b and c are on a closed path with the battery
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 13 // EQUI // 5 //
+11 12 13 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// The switch determines whether the path is open or closed.
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 12 13 // EQUI // 5 //
+3 <==> 14 // EQUI // 5 //
+5 6 <==> 15 16 // EQUI // 5 //
+7 <==> 7 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal is separated by a gap from terminal 4
+// Terminal 4 and the positive battery terminal are in the same electrical state
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 battery :
+7 terminal :
+8 are :
+9 in :
+10 the :
+11 same :
+12 electrical :
+13 state :
+
+
+1 2 3 4 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+5 6 <==> 8 // EQUI // 5 //
+
+
+
+
+
+// an incomplete circuit would not effect the the electrical state between the terminals.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 3 <==> 1 2 // EQUI // 5 //
+4 5 6 <==> 7 8 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 // EQUI // 5 //
+11 12 13 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// terminals 4, 5, and 6 are connected to the positive battery terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 7 <==> 6 7 // EQUI // 5 //
+8 9 10 11 12 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The path it was on
+// there is a path containing both Z and C
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+3 <==> 6 // EQUI // 5 //
+4 <==> 2 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// If the bulb is on the same closed path
+// The damaged bulb and the other bulb must be contained in the same path
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+4 <==> 8 9 10 // EQUI // 5 //
+5 6 7 8 9 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulb a was still contained in a closed path with the battery.
+// Bulb A was still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 7 8 9 <==> 6 7 8 9 10 // EQUI // 5 //
+10 11 12 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// If one bulb is removed, the others stop working
+// A and C are in the same closed path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+2 3 <==> 1 2 3 // EQUI // 5 //
+8 <==> 4 // EQUI // 5 //
+9 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// because all the terminals are connected to other terminals, an open switch disrupts that.
+// the open switch creates a gap
+
+
+1 the :
+2 open :
+3 switch :
+4 creates :
+5 a :
+6 gap :
+
+
+10 11 12 <==> 1 2 3 // EQUI // 5 //
+
+
+
+
+
+// There is a gap between the two bulb terminals
+// the terminals are separated by a gap
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+2 3 4 <==> 3 4 5 6 7 // EQUI // 5 //
+5 6 7 8 9 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// a short circuit has occured
+// there is a short circuit
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+1 2 3 <==> 3 4 5 // EQUI // 5 //
+4 5 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// there will be a gap at bulb b, thus affecting the rest of the circuit
+// bulb B creates a gap
+
+
+1 bulb :
+2 B :
+3 creates :
+4 a :
+5 gap :
+
+
+2 3 <==> 3 // EQUI // 5 //
+4 5 <==> 4 5 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// terminal 3 and the positie terminal are not connected.
+// Terminal 3 and the positive terminal are not connected
+
+
+1 Terminal :
+2 3 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 9 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// The positive battery terminal was not seperated by a gap from terminal 4.
+// Terminal 4 and the positive terminal are not separated by the gap
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+5 6 7 <==> 7 8 9 // EQUI // 5 //
+8 9 10 <==> 10 11 12 // EQUI // 5 //
+11 12 13 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is connected to the negative terminal.
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// A terminal is not connected to the positive battery terminal.
+// Terminals 1 and 2 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 5 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal and terminal 2 are seperated by a gap
+// Terminal 2 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+9 10 11 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// there is not gap between the terminals
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+2 3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// there is a gap between teh positive battery terminal and terminal 4.
+// Terminal 4 and the positive battery terminal are in the same electrical state
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 battery :
+7 terminal :
+8 are :
+9 in :
+10 the :
+11 same :
+12 electrical :
+13 state :
+
+
+2 <==> 8 // EQUI // 5 //
+5 6 7 8 9 10 11 12 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// The positive battery was not connected to terminal one.
+// Terminal 1 and the positive terminal are not connected
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 6 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and B will still be contained in a closed path to the battery.
+// bulbs A and B are still in closed paths with the battery
+
+
+1 bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 8 <==> 5 // EQUI // 5 //
+9 10 11 12 <==> 7 8 9 // EQUI // 5 //
+13 14 15 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the two components are seperated.
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+4 5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// because terminal 1 is directly connected to terminal 4
+// Terminals 1 and 4 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+2 3 <==> 1 2 3 4 // EQUI // 5 //
+4 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal and terminal 4 are connected
+// Terminal 4 and the positive terminal are connected
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 6 // EQUI // 5 //
+8 9 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 and terminal 2 are on the same side.
+// Terminals 1 and 2 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 connected :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 7 8 9 10 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// not connected to positive battery
+// Terminal 2 and the positive terminal are not connected
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// The battery uses a chemical reaction to maintain the voltage,
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 <==> 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+9 10 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Because the bulb does not have a closed path.
+// The bulb is not in the closed path containing the battery
+
+
+1 The :
+2 bulb :
+3 is :
+4 not :
+5 in :
+6 the :
+7 closed :
+8 path :
+9 containing :
+10 the :
+11 battery :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 5 6 <==> 3 4 // EQUI // 5 //
+7 8 9 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// there is a difference in electrical states
+// the terminals are separated by a gap
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 4 // EQUI // 5 //
+3 4 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to postive terminal of the battery
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 <==> 1 2 3 4 5 6 // EQUI // 5 //
+2 3 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is seperated from the positive terminal
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Battery is not contained i a closed path.
+// The battery in 4 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 3 4 <==> 5 6 // EQUI // 5 //
+5 6 7 8 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 was connected to the positive battery terminal
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+5 6 7 8 9 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// There are 2 paths in this diagram
+// there is a path containing A and a different path containing B and C
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A :
+7 and :
+8 a :
+9 different :
+10 path :
+11 containing :
+12 B :
+13 and :
+14 C :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// Because the switch was connected to the closed circuit
+// there is no path containing both switch Y and bulb A
+
+
+1 there :
+2 is :
+3 no :
+4 path :
+5 containing :
+6 both :
+7 switch :
+8 Y :
+9 and :
+10 bulb :
+11 A :
+
+
+2 3 <==> 6 // EQUI // 5 //
+4 5 <==> 2 // EQUI // 5 //
+6 7 8 9 <==> 1 // EQUI // 5 //
+
+
+
+
+
+// damaged bulb creates a gap.
+// a damaged bulb creates a gap
+
+
+1 a :
+2 damaged :
+3 bulb :
+4 creates :
+5 a :
+6 gap :
+
+
+1 2 <==> 1 2 3 // EQUI // 5 //
+3 <==> 4 // EQUI // 5 //
+4 5 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// that the battery connection does not work
+// there is a short circuit
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 6 7 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// because the terminals are not connected
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 3 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Terminal 5 is connected to teh positive battery terminal
+// Terminal 5 and the positive terminal are connected
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 was connected to the positive terminal
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// there is a gap between terminal one and two and the positive battery terminal
+// Terminals 1 and 2 are in the same electrical state
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 in :
+7 the :
+8 same :
+9 electrical :
+10 state :
+
+
+1 <==> 1 2 3 4 // EQUI // 5 //
+2 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c are contained on the same path with the battery
+// B and C are in the same path with the battery
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 // EQUI // 5 //
+11 12 13 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// because there is no closed path to the battery
+// the path is not closed
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+3 4 5 6 <==> 1 2 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 is not connected to the positive battery terminal
+// Terminal 1 and the positive terminal are not connected
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the battery is not in a closed bath alone
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 5 6 // EQUI // 5 //
+5 6 7 8 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// terminal 5 is connected to postive terminal of the battery
+// Terminal 5 and the positive terminal are connected
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// if x and z are closed then it will create a closed path
+// there is a path containing A, C, Z and X
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A, :
+7 C, :
+8 Z :
+9 and :
+10 X :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 <==> 6 7 8 9 10 // EQUI // 5 //
+8 <==> 2 // EQUI // 5 //
+11 12 13 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// positive terminal is serperated from terminal 2
+// Terminal 2 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the battery is not closed the bulb is.
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 5 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// there is not a gap in the connection
+// the terminals are not separated by a gap
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 separated :
+6 by :
+7 a :
+8 gap :
+
+
+2 3 <==> 3 4 5 // EQUI // 5 //
+4 5 <==> 6 7 8 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// if a bulb is in a closed circuit with a battery and a switch the switch will affect the bulb.
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+4 <==> 7 8 // EQUI // 5 //
+5 6 7 8 <==> 9 10 11 12 // EQUI // 5 //
+19 20 <==> 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c were contained in a closed path with the battery.
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 6 <==> 8 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 13 // EQUI // 5 //
+11 12 13 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// Because neither components are in closed paths.
+// Circuit 4 has no closed paths
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+4 <==> 3 // EQUI // 5 //
+5 6 7 <==> 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// you can see where the gap is
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+2 <==> 4 5 // EQUI // 5 //
+4 <==> 6 // EQUI // 5 //
+7 <==> 13 14 // EQUI // 5 //
+
+
+
+
+
+// if there is a gap in the circuit there the bulb will not light up.
+// A non-zero voltage means that the terminals are not connected.
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 the :
+7 terminals :
+8 are :
+9 not :
+10 connected. :
+
+
+3 <==> 4 // EQUI // 5 //
+12 13 14 15 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and Bulb B and the battery are in a closed path.
+// If C burns out, then A and B are still in a closed path with the battery.
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery. :
+
+
+1 2 3 4 5 6 7 8 <==> 6 7 8 // EQUI // 5 //
+9 <==> 9 10 // EQUI // 5 //
+10 11 12 13 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// That there is a gap
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+2 <==> 1 // EQUI // 5 //
+3 <==> 2 // EQUI // 5 //
+4 5 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// if the switch and bulb are contained in the same path, the switch will affect the bulb.
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 <==> 2 3 4 5 6 // EQUI // 5 //
+6 7 <==> 7 8 // EQUI // 5 //
+8 9 10 11 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Voltage is the difference between a positive and negative end on a battery.
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 4 // EQUI // 5 //
+5 6 7 8 9 10 11 12 13 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the path passes the energy through the switch
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+3 <==> 14 // EQUI // 5 //
+6 7 8 <==> 15 16 // EQUI // 5 //
+
+
+
+
+
+// that the bulb terminal and battery terminal are on the same side of a disconnected circut
+// The terminals are in the same state.
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+2 3 4 5 6 7 <==> 1 2 // EQUI // 5 //
+8 <==> 3 // EQUI // 5 //
+9 10 11 12 13 14 15 16 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Because the battery is not in a closed path.
+// The battery in 4 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 5 <==> 5 6 // EQUI // 5 //
+6 7 8 9 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// switch x is in the closed path with bulb a
+// Bulb A is still contained in a closed path with the battery and switch X.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 X. :
+
+
+1 2 <==> 10 11 12 13 14 15 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// There was a closed circuit
+// Bulb A is still contained in a closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery. :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 // EQUI // 5 //
+3 4 5 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// "because switch z is in bulb c""s closed path"
+// there is a path containing both Z and C
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 7 8 9 // EQUI // 5 //
+4 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// Bulb A was still in a closed path
+// Bulb A is still contained in a closed path with the battery and switch X.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 X. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+5 6 7 8 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Because there is a gap due to a damaged bulb.
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+1 <==> 1 2 3 4 5 // EQUI // 5 //
+3 <==> 6 7 // EQUI // 5 //
+4 5 <==> 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// Bulb A was still in a closed path with the battery
+// Bulb A was still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+5 6 7 8 <==> 6 7 8 9 10 // EQUI // 5 //
+9 10 11 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// The battery and light bulb are not contained in a close path
+// The battery in 4 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 3 4 5 <==> 1 2 // EQUI // 5 //
+6 7 8 <==> 5 6 // EQUI // 5 //
+9 10 11 12 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// and the circut is closed
+// A and C are in the same closed path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 <==> 1 2 3 // EQUI // 5 //
+4 5 <==> 4 // EQUI // 5 //
+
+
+
+
+
+// "becuase bulb C is on it""s own pathway."
+// Bulb C is in a separate path
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// if bulb A burns out then bulbs B and C will no longer be in a closed path.
+// If bulb A burns out, neither B nor C is in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 // EQUI // 5 //
+4 5 <==> 4 5 // EQUI // 5 //
+7 8 9 10 <==> 6 7 8 9 // EQUI // 5 //
+11 12 13 14 <==> 10 // EQUI // 5 //
+15 16 17 18 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is not connected to the positive terminal.
+// Terminal 1 and the positive terminal are not connected
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// because the battery is not in a closed circuit
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 5 <==> 5 6 // EQUI // 5 //
+6 7 8 9 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// the terminal it is connected to is not working
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 2 <==> 1 // EQUI // 5 //
+4 5 <==> 2 3 4 // EQUI // 5 //
+6 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// There must be a closed path and a battery.
+// there is a closed path containing both the bulb and a battery
+
+
+1 there :
+2 is :
+3 a :
+4 closed :
+5 path :
+6 containing :
+7 both :
+8 the :
+9 bulb :
+10 and :
+11 a :
+12 battery :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 // EQUI // 5 //
+4 5 6 7 8 9 <==> 3 4 5 6 7 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to terminal 6
+// Terminals 1 and 6 are not connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 not :
+7 connected :
+
+
+1 <==> 1 2 3 4 // EQUI // 5 //
+2 3 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// because bulb a is in a closed circuit with the battery and switch x
+// Bulb A is still contained in a closed path with the battery and switch X.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 X. :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 6 7 8 9 // EQUI // 5 //
+9 10 11 12 13 14 <==> 10 11 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// If the path is not closed, the switch will not affect the bbulb
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 15 16 // EQUI // 5 //
+4 5 <==> 7 // EQUI // 5 //
+7 8 <==> 12 13 // EQUI // 5 //
+9 10 11 <==> 14 // EQUI // 5 //
+
+
+
+
+
+// bulb b and c are on a closed path to the battery
+// If bulb A burns out, bulbs B and C are still in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 bulbs :
+7 B :
+8 and :
+9 C :
+10 are :
+11 still :
+12 in :
+13 a :
+14 closed :
+15 path :
+
+
+1 2 3 4 <==> 6 7 8 9 // EQUI // 5 //
+5 <==> 10 // EQUI // 5 //
+6 7 8 9 <==> 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// since a a gap does not affect the voltage of a battery
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+1 <==> 6 7 // EQUI // 5 //
+2 3 4 <==> 13 14 15 // EQUI // 5 //
+8 9 10 11 12 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Because there is a light bulb
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+3 <==> 5 6 // EQUI // 5 //
+4 5 6 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// the bulb will be burned out because the terminals
+// The damaged bulb and the other bulb must be contained in the same path
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+1 2 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+3 4 5 6 <==> 8 9 10 // EQUI // 5 //
+8 9 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Because the positive batter terminal and terminal 6 were connected.
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+2 3 4 5 6 7 8 <==> 1 2 3 4 5 6 // EQUI // 5 //
+9 10 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// because the the circuit is complete.
+// the path is not closed
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+2 3 4 <==> 1 2 // EQUI // 5 //
+5 6 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Bulbs B and C will still be on closed paths with the battery
+// bulbs B and C are still in closed paths with the battery
+
+
+1 bulbs :
+2 B :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the bulb is contained in an closed circuit
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 15 16 // EQUI // 5 //
+3 4 <==> 7 // EQUI // 5 //
+5 6 7 8 <==> 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// THE ARE ON THE SAME PATH
+// A and C are in the same path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+
+
+2 <==> 4 // EQUI // 5 //
+3 4 5 6 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// Bulb a and switch Y are not in the same path.
+// Switch Y and bulb A are not in the same closed path
+
+
+1 Switch :
+2 Y :
+3 and :
+4 bulb :
+5 A :
+6 are :
+7 not :
+8 in :
+9 the :
+10 same :
+11 closed :
+12 path :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 7 <==> 6 7 // EQUI // 5 //
+8 9 10 11 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// A chemical reaction inside the battery makes the electrical states of the positive and negative terminals different at all times.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 3 <==> 4 5 6 // EQUI // 5 //
+4 5 6 <==> 1 2 // EQUI // 5 //
+7 <==> 3 // EQUI // 5 //
+11 12 13 14 15 16 <==> 12 13 14 // EQUI // 5 //
+17 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// becasue the terminals 4,5, and 6 are connected to the positive terminal of the battery
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+2 3 4 5 6 <==> 1 2 3 4 5 // EQUI // 5 //
+7 8 <==> 6 7 // EQUI // 5 //
+9 10 11 12 13 14 15 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// switch Y does not effect bulb A
+// Switch Y and bulb A are not in the same closed path
+
+
+1 Switch :
+2 Y :
+3 and :
+4 bulb :
+5 A :
+6 are :
+7 not :
+8 in :
+9 the :
+10 same :
+11 closed :
+12 path :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+3 4 5 <==> 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb c creates a gap
+// If C burns out, then A and B are still in a closed path with the battery.
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery. :
+
+
+1 2 <==> 2 // EQUI // 5 //
+3 <==> 3 4 // EQUI // 5 //
+4 5 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Bulb C and the battery are not contained in a closed pathway
+// Bulb C was no longer in a closed path with the battery
+
+
+1 Bulb :
+2 C :
+3 was :
+4 no :
+5 longer :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 // EQUI // 5 //
+6 7 8 <==> 3 4 5 // EQUI // 5 //
+9 10 11 12 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the two terminals will both be 0
+// The terminals are in the same state.
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+1 2 3 <==> 1 2 // EQUI // 5 //
+6 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// bulb b is not in the same path with bulbs a and c.
+// Bulb B is in a separate path
+
+
+1 Bulb :
+2 B :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// The electrical state is interferred with.
+// A non-zero voltage means that the terminals are not connected.
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 the :
+7 terminals :
+8 are :
+9 not :
+10 connected. :
+
+
+1 2 3 <==> 1 2 3 // EQUI // 5 //
+6 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// Because the battery and the bulb are not in a closed path.
+// The battery in 4 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+2 3 4 5 6 <==> 1 2 // EQUI // 5 //
+7 8 <==> 5 6 // EQUI // 5 //
+9 10 11 12 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// "because by measuring voltage, you find the gap where there""s a difference in electrical states."
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+2 3 <==> 3 // EQUI // 5 //
+4 <==> 2 // EQUI // 5 //
+9 <==> 6 // EQUI // 5 //
+10 11 12 <==> 10 // EQUI // 5 //
+13 14 15 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// again, bulbs a and b will be contained on a closed path
+// If C burns out, then A and B are still in a closed path.
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 <==> 6 7 8 // EQUI // 5 //
+6 7 8 <==> 9 10 // EQUI // 5 //
+9 10 11 12 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c are contiained in the the same path with the battery.
+// A and C are not in the same path with the battery
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 5 // EQUI // 5 //
+7 8 9 10 11 <==> 6 7 8 9 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// There is a gap in the path.
+// Terminals 1 and 2 are in the same electrical state
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 in :
+7 the :
+8 same :
+9 electrical :
+10 state :
+
+
+1 <==> 1 2 3 4 // EQUI // 5 //
+2 <==> 5 // EQUI // 5 //
+5 6 7 <==> 6 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// bulb a is in a closed path with a battery
+// Bulb A is still in a closed path with the battery
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+8 9 10 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb C affect each other.
+// A and C are in the same closed path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 <==> 4 // EQUI // 5 //
+7 8 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// switch z is contained in a closed path
+// there is a path containing both Z and C
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+1 2 <==> 7 8 9 // EQUI // 5 //
+3 4 <==> 2 // EQUI // 5 //
+5 6 7 8 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// the bulb terminal and the negative battery terminal are separated by a gap
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+9 10 <==> 2 // EQUI // 5 //
+11 12 13 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and C are still in a closed path with the battery.
+// Bulbs A and C are still contained in closed paths with the battery
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 contained :
+8 in :
+9 closed :
+10 paths :
+11 with :
+12 the :
+13 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 8 9 10 <==> 8 9 10 // EQUI // 5 //
+11 12 13 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// if switch and bulb are contained in the same closed path
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 <==> 2 3 4 5 6 // EQUI // 5 //
+5 6 <==> 7 8 // EQUI // 5 //
+7 8 9 10 11 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// there is a gap between the positive battery connection and the bulb terminal.
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 9 10 11 12 13 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulb A is not on the same path that Bulb B and bulb C are.
+// there is a path containing A and a different path containing B and C
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A :
+7 and :
+8 a :
+9 different :
+10 path :
+11 containing :
+12 B :
+13 and :
+14 C :
+
+
+1 2 <==> 6 // EQUI // 5 //
+3 4 <==> 2 // EQUI // 5 //
+5 6 7 8 <==> 3 4 // EQUI // 5 //
+9 <==> 8 9 10 // EQUI // 5 //
+10 11 12 13 14 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// it runs on a different current
+// If C burns out, then A and B are still in a closed path with the battery.
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery. :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 3 4 // EQUI // 5 //
+3 4 5 6 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to the difference
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the batteries terminals are not connected
+// Circuit 4 has no closed paths
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+1 2 3 <==> 1 2 // EQUI // 5 //
+4 5 6 <==> 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because if there is a voltage that means there is a gap
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+5 6 <==> 2 // EQUI // 5 //
+7 <==> 4 5 // EQUI // 5 //
+8 <==> 3 // EQUI // 5 //
+9 <==> 6 // EQUI // 5 //
+11 12 <==> 13 14 // EQUI // 5 //
+
+
+
+
+
+// Find where there are different electrical states
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 6 // EQUI // 5 //
+5 6 7 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// circuit 2 is connected to the battery
+// there is no closed path containing the battery
+
+
+1 there :
+2 is :
+3 no :
+4 closed :
+5 path :
+6 containing :
+7 the :
+8 battery :
+
+
+1 2 <==> 1 // EQUI // 5 //
+3 4 <==> 2 // EQUI // 5 //
+5 6 7 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the gap in the circuit causes the circuit to be an open circuit
+// there is a gap in a circuit
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 a :
+7 circuit :
+
+
+1 2 <==> 1 // EQUI // 5 //
+3 4 5 <==> 5 6 7 // EQUI // 5 //
+9 10 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// there is a gap in the circuit
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 <==> 1 2 3 4 5 6 // EQUI // 5 //
+2 <==> 7 8 // EQUI // 5 //
+3 4 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the path has to be closed for the bulb to light up
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 8 9 10 11 // EQUI // 5 //
+7 8 9 <==> 15 16 // EQUI // 5 //
+
+
+
+
+
+// There is no gap so there is no difference in voltage
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+10 11 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Voltage is the difference between a positive and negative end on the battery.
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 <==> 1 2 3 4 5 6 // EQUI // 5 //
+2 <==> 7 8 // EQUI // 5 //
+3 4 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// bulb had a short circuit
+// there is a complete circuit
+
+
+1 there :
+2 is :
+3 a :
+4 complete :
+5 circuit :
+
+
+2 <==> 2 // EQUI // 5 //
+3 4 5 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb C are in a closed path with the battery.
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 <==> 6 7 8 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 13 // EQUI // 5 //
+11 12 13 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// Terminals 4, 5, and 6 are only connected to the positive battery terminal.
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+8 <==> 6 7 // EQUI // 5 //
+9 10 11 12 13 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the positive battery terminal
+// the terminals are not connected
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// because the terminals are in the same state
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 3 <==> 5 6 7 8 9 // EQUI // 5 //
+4 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// "because switch y isn""t included in bulb A""s closed path"
+// Switch Y and bulb A are not in the same closed path
+
+
+1 Switch :
+2 Y :
+3 and :
+4 bulb :
+5 A :
+6 are :
+7 not :
+8 in :
+9 the :
+10 same :
+11 closed :
+12 path :
+
+
+2 3 <==> 1 2 3 4 5 // EQUI // 5 //
+4 5 <==> 6 7 // EQUI // 5 //
+9 10 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the negative battery terminal is seperated by a gap from terminal 6
+// terminal 6 is separated by a gap from the negative battery terminal
+
+
+1 terminal :
+2 6 :
+3 is :
+4 separated :
+5 by :
+6 a :
+7 gap :
+8 from :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 <==> 8 9 10 11 12 // EQUI // 5 //
+5 6 <==> 3 4 // EQUI // 5 //
+7 8 9 <==> 5 6 7 // EQUI // 5 //
+10 11 12 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// that the bulb terminal is only connected to one of the battery terminals
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 <==> 1 // EQUI // 5 //
+5 <==> 2 3 4 // EQUI // 5 //
+8 9 10 11 12 13 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// there was a negavtive gap
+// terminal 4 is separated by a gap from the negative battery terminal
+
+
+1 terminal :
+2 4 :
+3 is :
+4 separated :
+5 by :
+6 a :
+7 gap :
+8 from :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 <==> 3 4 // EQUI // 5 //
+3 4 5 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to postive end of battery
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 <==> 1 2 3 4 5 // EQUI // 5 //
+2 3 <==> 6 7 // EQUI // 5 //
+4 5 6 7 8 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 is connected to the 1.5 volt battery.
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 9 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// The path must be closed
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+3 4 <==> 7 // EQUI // 5 //
+5 <==> 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Bulbs B and C are contained on the same path with the battery.
+// B and C are in the same path with the battery
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 // EQUI // 5 //
+11 12 13 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the positive terminal of the battery
+// Terminal 6 and the positive terminal are connected
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+3 4 <==> 7 8 // EQUI // 5 //
+5 6 7 8 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because a and b are in series and a and c are in parallel
+// If C burns out, then A and B are still in a closed path.
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+1 <==> 1 // EQUI // 5 //
+5 <==> 9 // EQUI // 5 //
+6 7 <==> 11 12 13 14 // EQUI // 5 //
+8 <==> 5 // EQUI // 5 //
+9 10 11 <==> 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the positive terminal of the battery
+// Terminal 5 and the positive terminal are connected
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+3 4 <==> 7 8 // EQUI // 5 //
+5 6 7 8 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// the bulb is not contained in the path
+// The bulb is not in the closed path containing the battery
+
+
+1 The :
+2 bulb :
+3 is :
+4 not :
+5 in :
+6 the :
+7 closed :
+8 path :
+9 containing :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// because positive charge is before gap
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+4 <==> 7 8 // EQUI // 5 //
+6 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Because it is not on the same path
+// If bulb A burns out, bulbs B and C are still in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 bulbs :
+7 B :
+8 and :
+9 C :
+10 are :
+11 still :
+12 in :
+13 a :
+14 closed :
+15 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 10 // EQUI // 5 //
+5 6 7 8 <==> 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// Seperate paths connected to the battery
+// If bulb A burns out, B and C are no longer in a closed path with the battery
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 B :
+7 and :
+8 C :
+9 are :
+10 no :
+11 longer :
+12 in :
+13 a :
+14 closed :
+15 path :
+16 with :
+17 the :
+18 battery :
+
+
+3 <==> 12 13 14 15 // EQUI // 5 //
+4 5 6 <==> 16 17 18 // EQUI // 5 //
+
+
+
+
+
+// A red X means the battery is in a short circuit.
+// there is a short circuit
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+1 2 3 <==> 1 // EQUI // 5 //
+7 <==> 2 // EQUI // 5 //
+8 9 10 11 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// The battery is not closed in a closed path.
+// Circuit 4 has no closed paths
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 5 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to the battery
+// Terminals 1, 2 and 3 are connected to the negative battery terminal
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+1 <==> 1 2 3 4 5 // EQUI // 5 //
+2 3 <==> 6 7 // EQUI // 5 //
+4 5 6 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and Bulb C are not contained in the same closed path
+// A and C are not in the same path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 8 <==> 4 5 // EQUI // 5 //
+9 10 11 12 13 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// bulbs A and C are not on the same closed path.
+// A and C are not in the same path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 5 // EQUI // 5 //
+7 8 9 10 11 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// bulb, battery, and switch are in closed path
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+5 <==> 7 8 // EQUI // 5 //
+6 7 8 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the paths of the circuit are no longer complete
+// there is an incomplete circuit
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+1 2 3 4 5 <==> 1 // EQUI // 5 //
+6 7 8 <==> 2 // EQUI // 5 //
+9 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// there is no closed path in circuit 4.
+// Circuit 4 has no closed paths
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+2 <==> 3 // EQUI // 5 //
+3 4 5 <==> 4 5 6 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// The battery keeps a chemical reaction reaction.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 7 8 // EQUI // 5 //
+4 5 6 7 <==> 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// There is always a difference in voltage between two battery terminals.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+2 <==> 3 // EQUI // 5 //
+3 <==> 1 2 // EQUI // 5 //
+4 5 6 7 <==> 9 10 11 // EQUI // 5 //
+8 9 10 11 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// terminal 1is connected to terminal 4
+// Terminals 1 and 4 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and B will still be in a contained path.
+// If C burns out, then A and B are still in a closed path.
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+7 <==> 9 // EQUI // 5 //
+8 9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulb a is in a closed circuit with the battery without the y switch.
+// Bulb A is still in a closed path with the battery
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+8 9 10 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// different paths with the battery
+// B and C are in the same path with the battery
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 5 6 7 8 // EQUI // 5 //
+3 4 5 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// "The electrical state at the terminal matches the battery""s electrical state"
+// terminal 1 is connected to the negative battery terminal
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+7 <==> 3 4 // EQUI // 5 //
+8 9 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Circuit 2 is not a short circuit because the battery is not in a closed path with itself.
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+9 10 <==> 1 2 // EQUI // 5 //
+11 12 <==> 5 6 // EQUI // 5 //
+13 14 15 16 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// Bulb A is on a closed circut path
+// Bulb A was still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 8 <==> 6 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// Bulb B and bulb C are contained in different paths with the battery
+// B and C are in the same path with the battery
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 <==> 4 // EQUI // 5 //
+8 9 10 <==> 5 6 7 8 // EQUI // 5 //
+11 12 13 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the battery always has a voltage because there is a positive terminal and there is a negative terminal.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+5 6 <==> 9 10 11 // EQUI // 5 //
+8 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// gap between 3 and positive battery
+// Terminal 3 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 3 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 <==> 9 10 11 // EQUI // 5 //
+2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because bulbs A and C are contained in different paths with the battery
+// A and C are in different paths with the battery
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 <==> 4 // EQUI // 5 //
+8 9 10 <==> 5 6 7 // EQUI // 5 //
+11 12 13 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// because of the gap at bulb b
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+1 2 3 4 <==> 13 14 15 // EQUI // 5 //
+5 6 7 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// because bulb c was in an open path
+// Bulb C was not in a closed path
+
+
+1 Bulb :
+2 C :
+3 was :
+4 not :
+5 in :
+6 a :
+7 closed :
+8 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// It is not a closed path.
+// the path is not closed
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+1 <==> 1 2 // EQUI // 5 //
+3 <==> 3 4 // EQUI // 5 //
+4 5 6 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// because switch y is not conatined in the closed path of bulb a and the battery.
+// Bulb A is still in a closed path with the battery
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+4 5 6 <==> 3 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 // EQUI // 5 //
+11 12 13 14 15 16 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// A terminal is not connected to the negative battery terminal.
+// Terminals 1 and 6 are not connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 not :
+7 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 5 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb B and C both still are on a closed path with the battery
+// bulbs B and C are still in closed paths with the battery
+
+
+1 bulbs :
+2 B :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 and terminal 6 are seperated by a gap
+// Terminals 1 and 6 are separated by the gap
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 separated :
+7 by :
+8 the :
+9 gap :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 7 <==> 5 6 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// because the battery is in a closed path.
+// the battery is contained in a closed path in which there is no bulb
+
+
+1 the :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 in :
+10 which :
+11 there :
+12 is :
+13 no :
+14 bulb :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// complete path including a battery and a bulb
+// there is a closed path containing both the bulb and a battery
+
+
+1 there :
+2 is :
+3 a :
+4 closed :
+5 path :
+6 containing :
+7 both :
+8 the :
+9 bulb :
+10 and :
+11 a :
+12 battery :
+
+
+1 2 <==> 1 // EQUI // 5 //
+3 <==> 6 // EQUI // 5 //
+4 5 6 7 8 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c creat a gap in the path
+// Bulb B is in a separate path
+
+
+1 Bulb :
+2 B :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+1 2 3 4 <==> 1 2 // EQUI // 5 //
+5 <==> 3 // EQUI // 5 //
+6 7 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal and terminal 5 are connected
+// Terminal 5 and the positive terminal are connected
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 6 // EQUI // 5 //
+8 9 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the the bulb terminal disconnected from the battery terminal
+// the terminals are not connected
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+1 2 3 4 <==> 1 2 // EQUI // 5 //
+5 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// the battery is contained in the circuit and the light bulb is not
+// the battery is contained in a path in which there is no bulb
+
+
+1 the :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 in :
+9 which :
+10 there :
+11 is :
+12 no :
+13 bulb :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 <==> 5 6 7 // EQUI // 5 //
+12 13 <==> 11 // EQUI // 5 //
+
+
+
+
+
+// because the two ends of the battery do not connect to one another
+// the battery is in an open path
+
+
+1 the :
+2 battery :
+3 is :
+4 in :
+5 an :
+6 open :
+7 path :
+
+
+5 6 7 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// When a switch is open the circuit is no longer complete
+// there is an incomplete circuit
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+4 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// if both bulbs are contained within a closed path
+// The damaged bulb and the other bulb must be contained in the same path
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+4 5 <==> 8 9 10 // EQUI // 5 //
+6 7 8 9 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// The bulb is in a closed circuit and the battery exists in that circuit
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+3 <==> 5 6 // EQUI // 5 //
+4 5 6 7 <==> 7 8 9 10 // EQUI // 5 //
+9 10 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the closed path is connected to the light bulb
+// Bulb A was still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 3 <==> 6 7 8 9 10 // EQUI // 5 //
+4 5 <==> 5 // EQUI // 5 //
+6 7 8 9 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// the electrical states between the terminals is the same, resulting in 0
+// The terminals are in the same state.
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+4 5 6 <==> 1 2 // EQUI // 5 //
+7 <==> 3 // EQUI // 5 //
+8 9 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb b and bulb c are contained within a closed path
+// B and C are in the same path with the battery
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 <==> 4 // EQUI // 5 //
+8 9 10 11 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// circuit 5 is in a closed path.
+// the battery is contained in a closed path in which there is no bulb
+
+
+1 the :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 in :
+10 which :
+11 there :
+12 is :
+13 no :
+14 bulb :
+
+
+1 2 <==> 13 14 // EQUI // 5 //
+3 <==> 3 4 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to terminal 1
+// Terminals 1 and 6 are separated by the gap
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 separated :
+7 by :
+8 the :
+9 gap :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// If bulb B is damaged there is a gap in the circuit
+// there is a gap in a circuit
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 a :
+7 circuit :
+
+
+7 <==> 2 // EQUI // 5 //
+8 9 <==> 3 4 // EQUI // 5 //
+10 11 12 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb a is in a complete circuit with the battery when switch z is closed.
+// Bulb A is still contained in a closed path with the battery and switch Z.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 Z. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 6 7 8 9 // EQUI // 5 //
+8 9 10 <==> 10 11 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// bulb a is on a closed path with the battery
+// Bulb A is still in a closed path with the battery
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+8 9 10 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// because those terminals are connected to the positive terminal of the battery.
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+4 5 <==> 6 7 // EQUI // 5 //
+6 7 8 9 10 11 12 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Not contained in a closed path
+// Bulb C was not in a closed path
+
+
+1 Bulb :
+2 C :
+3 was :
+4 not :
+5 in :
+6 a :
+7 closed :
+8 path :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+3 4 5 6 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal connected to positive charge
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 <==> 1 2 3 4 5 // EQUI // 5 //
+2 <==> 6 7 // EQUI // 5 //
+3 4 5 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// because voltage measures the difference between two points
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+4 5 6 7 8 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Bulbs a and c are in separate paths.
+// A, B and C are in different paths
+
+
+1 A, :
+2 B :
+3 and :
+4 C :
+5 are :
+6 in :
+7 different :
+8 paths :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 7 8 <==> 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to postive terminal of battery
+// Terminals 1 and 6 are not connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 not :
+7 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the negative battery terminal
+// the terminals are not connected
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Switch Z is in the same path as bulb A
+// Bulb A is still contained in a closed path with the battery and switch Z.
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 Z. :
+
+
+1 2 <==> 10 11 12 13 14 15 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 6 7 8 9 // EQUI // 5 //
+9 10 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// there will be a gap
+// If bulb A burns out, neither B nor C is in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+2 3 <==> 10 // EQUI // 5 //
+4 5 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// because each bulb has its own complete path
+// each bulb is in its own path
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c have separate paths within the closed circuit
+// If bulb A burns out, B and C are no longer in a closed path with the battery
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 B :
+7 and :
+8 C :
+9 are :
+10 no :
+11 longer :
+12 in :
+13 a :
+14 closed :
+15 path :
+16 with :
+17 the :
+18 battery :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+5 <==> 9 // EQUI // 5 //
+6 7 <==> 12 13 14 15 // EQUI // 5 //
+8 9 10 11 <==> 16 17 18 // EQUI // 5 //
+
+
+
+
+
+// A terminal is connected to a bulb.
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+3 4 <==> 6 7 // EQUI // 5 //
+5 6 7 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal has no gaps from terminal 4
+// Terminal 4 and the positive terminal are not separated by the gap
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+5 6 7 <==> 7 8 9 10 11 12 // EQUI // 5 //
+8 9 10 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// when a switch and bulb are whithin a closed path
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 <==> 2 3 4 5 6 // EQUI // 5 //
+6 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// because the path is short
+// the path is not closed
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Bulb A will no longer be completing the circuts.
+// If bulb A burns out, neither B nor C is in a closed path
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 2 <==> 2 3 // EQUI // 5 //
+4 5 <==> 6 7 8 9 // EQUI // 5 //
+6 7 <==> 10 // EQUI // 5 //
+8 9 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Bulb C will create a gap in the path
+// each bulb is in its own path
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+7 8 9 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb a was contained on a closed path with the battery
+// Bulb A was still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 5 // EQUI // 5 //
+5 6 7 8 <==> 6 7 8 9 10 // EQUI // 5 //
+9 10 11 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is connected to terminl 4.
+// Terminals 1 and 4 are connected
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and B are not on the same path as Bulb C.
+// Bulb C is in a separate path
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+5 6 <==> 3 // EQUI // 5 //
+7 8 9 10 <==> 4 5 6 7 // EQUI // 5 //
+12 13 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Each circuit must have a connection.
+// there is a complete circuit
+
+
+1 there :
+2 is :
+3 a :
+4 complete :
+5 circuit :
+
+
+1 2 <==> 1 // EQUI // 5 //
+3 4 <==> 2 // EQUI // 5 //
+5 6 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// A switch contained in a closed path with a bulb and a battery will affect the bulb.
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 1 // EQUI // 5 //
+4 5 6 7 <==> 8 9 10 11 // EQUI // 5 //
+14 15 <==> 14 // EQUI // 5 //
+16 17 <==> 15 16 // EQUI // 5 //
+
+
+
+
+
+// Voltage is the difference between a positive and negative terminal on the battery.
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 <==> 1 2 3 4 5 6 // EQUI // 5 //
+2 <==> 7 8 // EQUI // 5 //
+3 4 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c were in a closed paty with the battery.
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 <==> 6 // EQUI // 5 //
+6 7 8 9 <==> 9 10 11 12 13 // EQUI // 5 //
+10 11 12 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// can complete the path by having z be closed
+// there is a path containing A, C, Z and X
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A, :
+7 C, :
+8 Z :
+9 and :
+10 X :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 5 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+7 <==> 6 7 8 9 10 // EQUI // 5 //
+8 9 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// A switch will affect a bulb it the bulb and the switch are in the path as the battery
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+7 <==> 1 // EQUI // 5 //
+8 9 10 11 12 <==> 2 3 4 5 6 // EQUI // 5 //
+13 <==> 7 8 // EQUI // 5 //
+14 15 16 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal is not connected
+// There is no gap between terminal 6 and the positive terminal
+
+
+1 There :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 terminal :
+7 6 :
+8 and :
+9 the :
+10 positive :
+11 terminal :
+
+
+1 2 3 4 <==> 1 // EQUI // 5 //
+5 6 7 <==> 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb C are still on a closed path that contains the battery.
+// Bulbs A and C are still in closed paths with the battery
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 5 // EQUI // 5 //
+7 <==> 6 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+13 14 15 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and C will still be on their own completed circuts.
+// Bulbs A and C are in a closed path
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 in :
+7 a :
+8 closed :
+9 path :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// The damaged bulb B has left a gap in the path so the charge can not reach it
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+1 2 3 4 <==> 8 9 10 11 12 // EQUI // 5 //
+7 8 <==> 13 14 15 // EQUI // 5 //
+12 <==> 6 7 // EQUI // 5 //
+
+
+
+
+
+// the terminal is separated from the battery terminal
+// the terminals are separated by a gap
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to another terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+3 4 <==> 6 7 // EQUI // 5 //
+5 6 7 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulb A is connected to switch Z
+// There is no path containing both switch Y and bulb A
+
+
+1 There :
+2 is :
+3 no :
+4 path :
+5 containing :
+6 both :
+7 switch :
+8 Y :
+9 and :
+10 bulb :
+11 A :
+
+
+3 4 <==> 2 // EQUI // 5 //
+5 6 7 <==> 7 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// there is a closed path, with switch z, that contains bulb a and the battery
+// there is a path containing A, C, Z and the battery
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A, :
+7 C, :
+8 Z :
+9 and :
+10 the :
+11 battery :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 2 // EQUI // 5 //
+3 4 5 <==> 3 4 // EQUI // 5 //
+10 <==> 5 // EQUI // 5 //
+11 12 13 14 15 <==> 6 7 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Terminal 4, terminal 5, and terminal 6 are connected to the positive terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 // EQUI // 5 //
+8 9 <==> 6 7 // EQUI // 5 //
+10 11 12 13 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Circuit 2 is not a short circuit because the battery is not connected to itself.
+// The battery in 2 is not in a closed path
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+3 4 <==> 5 6 // EQUI // 5 //
+5 6 7 <==> 7 8 9 10 // EQUI // 5 //
+9 10 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Because terminal 1 is seperated from the positive battery terminal.
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 <==> 9 10 11 // EQUI // 5 //
+2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// bulb a and bulb c are contained in different paths with the bttery.
+// A and C are in different paths with the battery
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 <==> 4 // EQUI // 5 //
+8 9 10 <==> 5 6 7 // EQUI // 5 //
+11 12 13 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// because bulb a is in a closed path with the battery.
+// Bulb A is still in a closed path with the battery
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+9 10 11 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal is connected to the bulb
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 8 // EQUI // 5 //
+6 7 8 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// because bulb a is in a closed path, and bulb c is in a closed path.
+// Bulbs A and C are still in closed paths
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+
+
+1 <==> 5 // EQUI // 5 //
+2 3 <==> 1 2 3 4 // EQUI // 5 //
+12 13 14 15 16 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// The positive terminal has 1.5 V
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 <==> 7 8 // EQUI // 5 //
+5 6 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// because of the chemical in the battery
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 3 4 <==> 4 5 6 // EQUI // 5 //
+5 6 7 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Both components need to be in closed paths.
+// the bulb and the battery are in a closed path
+
+
+1 the :
+2 bulb :
+3 and :
+4 the :
+5 battery :
+6 are :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+3 4 5 <==> 6 // EQUI // 5 //
+6 7 8 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// bulb a and bulb c are wired in parallel
+// A and C are in different paths
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 <==> 4 // EQUI // 5 //
+8 9 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulb terminals 3 and 4
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// the other bulb will not light.
+// The damaged bulb and the other bulb must be contained in the same path
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+1 2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+4 5 6 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// because there was a gap in the terminals
+// there is no path containing both switch Y and bulb A
+
+
+1 there :
+2 is :
+3 no :
+4 path :
+5 containing :
+6 both :
+7 switch :
+8 Y :
+9 and :
+10 bulb :
+11 A :
+
+
+2 <==> 1 // EQUI // 5 //
+3 <==> 2 // EQUI // 5 //
+4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 <==> 6 // EQUI // 5 //
+
+
+
+
+
+// if the switch is open in a path with the battery and bulb.
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 4 5 6 // EQUI // 5 //
+4 <==> 7 8 // EQUI // 5 //
+6 7 8 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// 4, 5, and 6 are connected to the positive side
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 6 <==> 6 7 // EQUI // 5 //
+7 8 9 10 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// a voltage reading of 0 volts indicates a gap in the circuit.
+// there is no gap between the terminals
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 2 3 <==> 1 // EQUI // 5 //
+7 <==> 2 // EQUI // 5 //
+8 9 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// 4 5 and 6 are not connected to negative battery terminal
+// Terminals 4, 5 and 6 are not connected to the negative battery terminal
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 not :
+8 connected :
+9 to :
+10 the :
+11 negative :
+12 battery :
+13 terminal :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 6 7 <==> 6 7 8 // EQUI // 5 //
+8 9 10 11 <==> 9 10 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// bulbs a and b are still contained on a closed path with the battery
+// If C burns out then A and B are still in a closed path with the battery
+
+
+1 If :
+2 C :
+3 burns :
+4 out :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+5 <==> 9 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+7 <==> 3 4 // EQUI // 5 //
+8 9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+12 13 14 <==> 15 16 17 // EQUI // 5 //
+
+
+
+
+
+// bulbs a, b, and c are all in the same path.
+// A and C are in the same path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 <==> 4 // EQUI // 5 //
+8 9 10 11 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// a and c are on the same closed path with the battery
+// A and C are in the same closed path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 2 3 <==> 1 2 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+5 6 7 8 9 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// "if the switch is included in the bulb""s closed path, then the switch being open will affect the bulb"
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 // EQUI // 5 //
+9 10 <==> 8 9 10 11 // EQUI // 5 //
+12 13 <==> 12 13 // EQUI // 5 //
+16 17 <==> 14 // EQUI // 5 //
+18 19 <==> 15 16 // EQUI // 5 //
+
+
+
+
+
+// because the outcome of the bulb will not affect each other
+// A and C are not in the same path with the battery
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+4 5 6 <==> 6 7 8 9 // EQUI // 5 //
+7 8 9 <==> 4 5 // EQUI // 5 //
+
+
+
+
+
+// not seperated by a gap
+// Terminal 6 and the positive terminal are not separated by the gap
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+1 2 <==> 7 8 9 // EQUI // 5 //
+3 4 5 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// because terminal 1 and the neavtive terminal are seperated.
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+2 3 4 5 6 7 <==> 1 2 3 4 5 6 // EQUI // 5 //
+8 9 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Because their is a gap between A and C now.
+// there is an incomplete circuit
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+3 <==> 2 // EQUI // 5 //
+4 5 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb b are still contained in closed paths with the battery
+// If C burns out then A and B are still in a closed path with the battery
+
+
+1 If :
+2 C :
+3 burns :
+4 out :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery :
+
+
+1 2 3 4 5 <==> 6 7 8 // EQUI // 5 //
+6 <==> 9 // EQUI // 5 //
+7 <==> 10 // EQUI // 5 //
+8 <==> 3 4 // EQUI // 5 //
+9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+12 13 14 <==> 15 16 17 // EQUI // 5 //
+
+
+
+
+
+// B and C are not in the same circuit as A.
+// each bulb is in its own path
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+4 5 <==> 3 // EQUI // 5 //
+6 7 8 9 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// there terminals are separated by a gap when the voltage jumps from 0 to 1.5.
+// the terminals are separated by a gap
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulbs a b and c are on a closed path
+// A and C are in the same closed path
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 <==> 4 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// I think the red X means that this is dangerous and should never happen unless something is seriously wrong.
+// there is a short circuit
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+1 <==> 1 // EQUI // 5 //
+9 <==> 2 // EQUI // 5 //
+10 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// because there was no gap from the positive terminal of the battery
+// Terminal 1 and the positive terminal are separated by the gap
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+3 <==> 7 8 // EQUI // 5 //
+4 5 <==> 9 10 11 // EQUI // 5 //
+6 7 8 9 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulbs A and B are still connected to the closed path containing the battery
+// If C burns out then A and B are still in a closed path with the battery
+
+
+1 If :
+2 C :
+3 burns :
+4 out :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+5 <==> 9 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+7 <==> 3 4 // EQUI // 5 //
+8 9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+12 13 14 <==> 15 16 17 // EQUI // 5 //
+
+
+
+
+
+// if the switch and the bulb are in the same path
+// When the switch and the bulb are contained in the same path
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 6 <==> 2 3 4 5 6 // EQUI // 5 //
+7 <==> 7 8 // EQUI // 5 //
+8 9 10 11 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulb c and switch z are in the same closed path
+// there is a path containing both Z and C
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+1 2 3 4 5 <==> 7 8 9 // EQUI // 5 //
+6 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// the bulb only has one terminal connected
+// The battery is contained in a path which does not contain any other components
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 which :
+9 does :
+10 not :
+11 contain :
+12 any :
+13 other :
+14 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 <==> 9 10 11 // EQUI // 5 //
+5 6 <==> 5 6 7 // EQUI // 5 //
+7 <==> 12 13 14 // EQUI // 5 //
+
+
+
+