P 3.8-4 The circuit of Figure P 3.8-4 represents an auto’s electrical system. A report states that i_H = 9 A, i_B = –9 A, and i_A = 19.1 A. Verify that this result is correct.

Hint: Verify that KCL is satisfied at each node and that KVL is satisfied around each loop.

Figure P 3.8-4

Using the given values, at the left node we should have

Clearly the currents are wrong. Write out Kirckhoff’s laws

Junction Rule

First Loop (top loop, start at lower left go CW)

Second Loop (bottom loop, start at lower left go CW)

So rewrite these equations into standard form

Now put these equations into MATLAB and get solution

Ans =

'iA = 16.7568 A'

'iB = -6.4865 A'

'iH = 10.2703 A'

Clearly the report was wrong!

MATLAB Code follows:

%Program to solve PH 320 Homework Problem P3.8-4

%version 2019-01-21 DW Donovan

clear all;

RR = [1 1 -1;0 0.05 1.2;0.1 -0.05 0];

VV = [0 12 2]';

ii = RR\VV;

ia = ii(1);

ib = ii(2);

iH = ii(3);

Ans = {['iA = ' num2str(ia) ' A']

['iB = ' num2str(ib) ' A']

['iH = ' num2str(iH) ' A']}

%{

Ans =

'iA = 16.7568 A'

'iB = -6.4865 A'

'iH = 10.2703 A'

%}

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This page last updated on January 21, 2019