P 5.4-4 Find the Thévenin equivalent circuit for the circuit shown in Figure P 5.4-4.

Figure P 5.4-4

To find the Thevenin equivalent circuit we need the , Thevenin resistance and the open circuit voltage at a-b, . We get the Thevenin Resistance by deactivating the power sources and finding the resistance between a and b. Deactivating the 18 V supply leaves us with the circuit

We can see the 6 Ω and the 3 Ω resistors are in parallel and can be replaced by the equivalent resistance

So the circuit now looks like

We can add the 2 Ω and the 10 Ω in series and we have

Combining the two 12 Ω in parallel provides a Thevenin resistance of

So

Now to get we take our circuit, identify mesh currents

Do a voltage walk to find

Write out Mesh Equations

Use MATAB to solve for , , and use those to solve for

And the Thevenin Circuit looks like

MATLAB Work Follows:

%Program to solve PH 320 Homework Problem P5.4-4

%version 2019-03-06 DW Donovan

clear all;

RR = [(12 + 6 + 10) -(6);

-(6) (6 + 3)];

VV = [0 18]';

II = RR\VV;

i1 = II(1);

i2 = II(2);

voc = 3*i2+10*i1;

Ans = {['i1 = ' num2str(i1) ' A'];

['i2 = ' num2str(i2) ' A'];

['voc = ' num2str(voc) ' V']};

Ans

%{

Ans =

'i1 = 0.5 A'

'i2 = 2.3333 A'

'voc = 12 V'

%}

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This page last updated on March 6, 2019