Question

Problem 4: The equations describing the circuit shown in Figure P38 are -1RiRi4 = 0 -Rii4+ Rziz + Rsis 0 -Rsis +Raia + v2 = 0 i=12+i 100 V. (Note The given values of the resistances and the voltage v, are R,-5. R, - 100, R that 1 kn 1000 n) Suppose that each resistance is rated to carry a current of no more than 1 mA (= 0.001 A). Determine the allowable range of positive values for the voltage v 150, R 250 kO, and v, 200, R4 Figure P38

Solve using Matlab

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Answer 1

Re-writing the equations:

$R_{1}i_{1}+0i_{2}+0i_{3}+R_{4}i_{4}+0i_{5}=v_{1}$

$0i_{1}+R_{2}i_{2}+0i_{3}-R_{4}i_{4}+R_{5}i_{5}=0$

$0i_{1}+0i_{2}-R_{3}i_{3}+0i_{4}+R_{5}i_{5}=v_{2}$

$i_{1}-i_{2}+0i_{3}-i_{4}+0i_{5}=0$

$0i_{1}+i_{2}-i_{3}+0i_{4}-i_{5}=0$

There are five equations and five unknows which can be solved using matrices in MATLAB. For different positive values of v₂ we will find the magnitude of currents and select only those values of voltages for which magnitudes of all the currents are less than 0.001 A. The MATLAB code is given below:

v=0:0.1:100;V=0;
A=1000*[5 0 0 150 0;0 100 0 -150 250;0 0 -200 0 250;1 -1 0 -1 0;0 1 -1 0 -1];
for i=1:length(v)
B=[100;0;v(i);0;0];
I=B\A;
if (abs(I)<=0.001) %condition to check whether the currents are lower than 0.001 A
V=[V v(i)]; %valid values of v2 for which all the currents are lower than 1 mA
end
end

The result is 'V' which shows that for no positive value of v₂, all the currents will be lower than 1 mA.