Question

For each circuit shown in the figure, find the current through and potential difference across each resistor

4Ω 6Ω 24 V 24 Ω 812 24 Ω

Thank you!

Answer 1

Loop 1

18*I1 -6*I2-8*I3 = 24

LOOP 2

-6I1 + 54I2 -24I3= 0

LOOP 3

-8 I1 -24I2 +32 I3 =0

putting this in matrix form we have

[18,-6,-8; -6,54,-24;-8,-24,32][I1,I2,I3]=[24,0,0]

USING CRAMER'S

system determinant =[18,-6,-8; -6,54,-24;-8,-24,32]=13824

I1 determinant = [24 0 0; -6,54,-24;-8,-24,32]=20736

12 deter=[18,-6,-8; 24,0,0;-8,-24,32]=2016

13 deter=[18,-6,-8; -6,54,-24;24,0,0]=13824

i1 = 20736/13824= 1.5A

I2 =2016/13824=0.15A

i3 =13824/13824 = 1A

Loop 1 circuit

V4ohms = 4*1.5 =6V

6 ohms resistor I = 1.35 V= 1.35 *6 =8.1V

8 ohms resistor I = 0.5V= 0.5 *8 =4V

Loop 2 circuit

First 24 0hms i=0.15A V=24*0.15=3.6V

2nd 24 ohms I= 1-0.15=0.85A V= 0.85*24=20.4V

6 ohms I = 1.35    V=1.35*6= 8.1V

Loop 3 circuit

24ohns= I = 0.85   V =0.85*24=20.4V

8ohms I =1-1.5=-0.5*8 =4V