# Circuit Theory/Variables and Units

## Electric Charge (Coulombs)

**Electric charge** is a physical
property of
matter that causes it to experience a
force when near other electrically charged
matter. Electric Charge (symbol q) is measured in SI units called
**\"Coulombs\"**, which are abbreviated with the letter capital C.

We know that q=n\*e, where n = number of electrons and e= 1.6\*10^−19^.
Hence n=1/e coulombs. A Coulomb is the total charge of
6.24150962915265×10^18^ electrons, thus a single electron has a charge
of −1.602 × 10^−19^ C.

It is important to understand that this concept of \"charge\" is
associated with static electricity. Charge, as a concept, has a physical
boundary that is related to counting a group of electrons. \"Flowing\"
electricity is an **entirely different
situation**.
\"Charge\" and electrons separate. Charge moves at the speed of light
while electrons move at the speed of **1
meter/hour**. Thus in most circuit
analysis, \"charge\" is an abstract concept unrelated to energy or an
electron and more related to the flow of
**information**.

Electric charge is the subject of many fundamental laws, such as
**Coulomb\'s Law** and **Gauss\'
Law** (static electricity) but is not used
much in circuit theory.

## Voltage (Volts)

**Voltage** is a measure of the work required to move a charge from one
point to another in a electric field. Thus the unit \"volt\" is defined
as a Joules (J) per Coulomb (C).

$$V = \frac{W}{q}$$

W represents work, q represents an amount of charge. Charge is a static
electricity concept. The definition of a volt is shared between static
and \"flowing\" electronics.

Voltage is sometimes called \"electric potential\", because voltage
represents the a difference in Electro Motive Force (EMF) that can
produce current in a circuit. More voltage means more potential for
current. Voltage also can be called \"Electric Pressure\", although this
is far less common.

Voltage is not measured in absolutes but in *relative* terms. The
English language tradition obscures this. For example we say \"What is
the distance to New York?\" Clearly implied is the relative distance
from where we are standing to New York. But if we say \"What is the
voltage at \_\_\_\_\_\_?\" What is the starting point?

Voltage is defined between two points. Voltage is relative to where 0 is
defined. We say \"The voltage from point A to B is 5 volts.\" It is
important to understand EMF and voltage are two different things.

When the question is asked \"What is the voltage at \_\_\_\_\_\_?\",
look for the ground symbol on a circuit diagram. Measure voltage from
ground to \_\_\_\_\_. If the question is asked \"What is the voltage
from A to B?\" then put the red probe on A and the black probe on B (not
ground).

The absolute is referred to as \"EMF\" or Electro Motive Force. The
difference between the two EMF\'s is a voltage.

## Current (Amperes)

**Current** is a measurement of the flow of electricity. Current is
measured in units called **Amperes** (or \"Amps\"). An ampere is
\"charge volume velocity\" in the same way water current could be
measured in \"cubic feet of water per second.\" But current is a **base
SI unit**, a fundamental dimension of
reality like space, time and mass. A coulomb or charge is not. A coulomb
is actually defined in terms of the ampere. \"Charge or Coulomb\" is a
**derived SI
Unit**.
The coulomb is a fictitious entity left over from the **one fluid /two
fluid**
philosophies of the 18th century.

This course is about flowing electrical energy that is found in all
modern electronics. Charge volume velocity (defined by current) is a
useful concept, but understand it has no practical use in engineering.
Do not think of current as a bundle electrons carrying energy through a
wire. Special relativity and quantum
mechanics concepts are necessary to
understand how electrons move at **1
meter/hour** through copper, yet
electromagnetic energy moves at near the speed of light.

Amperes are abbreviated with an \"A\" (upper-case A), and the variable
most often associated with current is the letter \"i\" (lower-case I).
In terms of coulombs, an ampere is:

$$i = \frac{dq}{dt}$$

Because of the widespread use of complex numbers in Electrical
Engineering, it is common for electrical engineering texts to use the
letter \"j\" (lower-case J) as the imaginary number, instead of the
\"i\" (lower-case I) commonly used in math texts. This wikibook will
adopt the \"j\" as the imaginary number, to avoid confusion.

## Energy and Power

Electrical theory is about energy storage and the flow of energy in
circuits. Energy is chopped up arbitrarily into something that doesn\'t
exist but can be counted called a coulomb. Energy per coulomb is
voltage. The velocity of a coulomb is current. Multiplied together, the
units are energy velocity or power \... and the unreal \"coulomb\"
disappears.

### Energy

Energy is measured most commonly in Joules, which are abbreviated with a
\"J\" (upper-case J). The variable most commonly used with energy is
\"w\" (lower-case W). The energy symbol is w which stands for work.

From a thermodynamics point of view, all energy consumed by a circuit is
work \... all the heat is turned into work. Practically speaking, this
can not be true. If it were true, computers would never consume any
energy and never heat up.

The reason that all the energy going into a circuit and leaving a
circuit is considered \"work\" is because from a thermodynamic point of
view, electrical energy is ideal. All of it can be used. Ideally all of
it can be turned into work. Most introduction to thermodynamics courses
assume that electrical energy is completely organized (and has entropy
of 0).

### Power

A corollary to the concept of energy being work, is that all the
energy/power of a circuit (ideally) can be accounted for. The sum of all
the power entering and leaving a circuit should add up to zero. No
energy should be accumulated (theoretically). Of course capacitors will
charge up and may hold onto their energy when the circuit is turned off.
Inductors will create a magnetic field containing energy that will
instantly disappear back into the source through the switch that turns
the circuit off.

This course uses what is called the
\"passive\" sign
convention for power. Energy put into a circuit by a power supply is
negative, energy leaving a circuit is positive.

Power (the flow of energy) computations are an important part of this
course. The symbol for power is w (for work) and the units are Watts or
W.
