Using the values given below find the currents shown in the

Using the values given below, find the currents shown in the diagram. R_1 = 31_ohm R_2 = 31_ohm R_3 = 43_ohm R_4 = 39_ohm V_1 = 9.1_V V_2 = 13_V V_3 = 13_V I_1 =___I_2 =___I_3 =___

Solution

Applying kirchoffs voltage law in the upper loop

V1 - I1R1 - I3R3 - V3 = 0

substituting the values we get   

31 I1 + 43I3 = -3.9.......(1)

Applying kirchoffs voltage law in the LOWER loop

-V2 - I2R2 -I2R4 +V3 + I3R3 = 0

substituting the values we get

70 I2 - 43I3 = 0 ......(2)

applying junction law in the right arm middle junction of the circuit

I1 = I2 + I3....(3)

solving 1 , 2 ,3 we get

I1 = 0.0677

I2 = 0.0258

I3 = 0.0419