Resistors R1, R2, R3, and R4 are arranged in a circuit as shown in the figure ab

Question

         

Resistors R1, R2, R3, and R4 are arranged in a circuit as shown in the figure above. The direction of positive currents I1, I2, I3, and I4 through the resistors are shown. (i.e., negative current values correspond to currents in the opposite direction to that shown above). The values for the resistors and the batteries in the circuit are: R1 = 100 ?, R2 = 200 ?, R3 = 30 ?, R4 = 400 ?, V1 = 4 V, and V2 = 12 V. What is the value of I2, the current through R2? (remember I2 is a signed number) I2 =

Explanation / Answer

V1 =4

asume 0V on the negative side and 4V on the positive side of battery

V1 = 4-100I1

4-100I1-0 = 30I3

4-100I1 = 30I3

4-100I1+12 = 200I2

4-100I1 + 12 - 0 = 400I4

4 - 100I1 + 12 = 400I4

I1 = I2 + I3

(16 - 200I2)/100 = I2 + (12-200I2)/30

480 - 6000I2 = 3000I2 + 1200 - 20000I2

11000I2 = 720

I2 = 720/11000 = 0.0654 A

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