P 8.3-14 The circuit shown in Figure P 8.3-14 is at steady state when the switch closes at time t = 0. Determine i(t) for t ≥ 0.

 

P8_3_14

Figure P 8.3-14

 

Again the standard form of the current in the inductor is

 

 

So just before the switch is thrown the circuit is in steady state, so the inductor looks like a short circuit and the whole circuit looks like

So we have two resistors in parallel the 5 Ω and 20 Ω as the 18 Ω resistor is shorted out.  i(t) is pointing in the opposite direction as the current will be flowing.  This current is the current that flows through the 20 Ω.  So using current division

 

So

 

After the switch is thrown and again waiting for a long time so that we are in steady state again the circuit with some annotations would now look like

Now we find the  which is the labeled i(t) or i4 by doing a mesh analysis with the identified currents.

 

 

 

Put these into standard matric form

 

 

 

 

 

Plugging this into MATLAB yields

ans =

 

    'i1 = -2 A'

    'i2 = 1.3333 A'

    'i3 = 0.66667 A'

    'i4 = 0.66667 A'

 

So the long term current through the inductor is

 

 

Deactivating power sources so that we can find the Thevenin Resistance we have a circuit

So we have the 5 Ω and 20 Ω resistors in parallel.  Combining them we get

 

 

So the circuit now is

The 4 Ω and 5 Ω are in series so we can replace them with  a 9 Ω Resistor and the circuit looks like

 

So the Thevenin resistance is

 

 

So

Plugging in to the standard form

 

 

 

 

MATLAB Code and work Follows:

 

%Program to solve PH 320 Homework Problem P8.3-14

%version 2019-07-08 DW Donovan

clear all;

 

RR = [1 0 0 0;

    0 (20 + 5) -(20) 0;

    -(5) -(20) (20 + 5 + 18) -(18);

    0 0 -18 18];

 

VV = [-2 20 0 0]';

 

II = RR\VV;

i1 = II(1);

i2 = II(2);

i3 = II(3);

i4 = II(4);

 

 

ans ={['i1 = ' num2str(i1) ' A']; ['i2 = ' num2str(i2) ' A'];

    ['i3 = ' num2str(i3) ' A']; ['i4 = ' num2str(i4) ' A']};

 

ans

 

%{

ans =

 

    'i1 = -2 A'

    'i2 = 1.3333 A'

    'i3 = 0.66667 A'

    'i4 = 0.66667 A'

%}

 

 

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on July 8, 2019