# Circuit Theory/Lab4.5.1

!the original circuit, R7 is the load, find thevenin equivalent of the
rest of the
circuit
!Finding Vth using ohm\'s
law !thevenin resistance
is calculated by zeroing the sources and opening the
load
!redrawing thevenin resistance network to make calculation
easier

Example, find the thevenin equivalent of this circuit, treating R7 as
the load.

-   Simulate the circuit, displaying load voltage and current as the
    load is swept through a range of resistance values
-   Simulate the thevenin equivalent circuit and again sweep the load
    voltage and current through a range of resistance values

## Finding Thevenin Voltage

Open the load (resistor R7), and find the voltage across it\'s
terminals.

R~5~ and R~6~ are dangling and can be removed.

V~th~ = V~A~ - V~B~

V~A~ = 2-V~R1~ = 2 - (2-5)\*2.2/(2.2+4.7) .. voltage divider

V~A~ = 2.9565

V~B~ = 5-V~R3~ = 5 - 5\*6.8/(6.8+6.8) .. voltage divider

V~B~ = 2.5 volts

V~th~ = 2.9565 - 2.5 = 0.4565 volts

Can check with this
simulation.

## Finding Thevenin Resistance

Remove the load, zero the sources.

Redraw up and down so the parallel/serial relationships between the
resistors are obvious.

-   $R_{th} = 1 + \frac{1}{\frac{1}{2.2} + \frac{1}{4.7}} + \frac{1}{\frac{1}{6.8} + \frac{1}{6.8}} + 1.5$
-   $R_{th} =  7.3986$

## Finding Norton Current

I~N~ = V~th~/R~th~ = 0.4565/7.3986 = 0.0617 amp

## Simulating the original circuit

In the
simulation,
can see the computed Norton\'s current when the load is 0 ohms.

Can see the computed Thevenin voltage when the load is around 20 ohms
which approximates an open.

## Comparing with the Thevenin Equivalent

In this
simulation,
can see the same values, except this time the load voltage is relative
to ground, so don\'t have to look at a drop or differences between two
voltages as with the original circuit simulation.

<File:Example25e.png%7CSweep> simulation of original circuit for R7
values of 47 ranging from 0 to 20 <File:Example25f.png%7CThe> thevenin
equivalent with the R7 load in place <File:Example25g.png%7CSweep>
simulation of the thevenin equivalent circuit for R7 values ranging from
0 to 20 ohms

