Two loops share a resistor between points A and B

PHYSICS · Subjective · CBSE · Physics · Current Electricity · Current Electricity

Problem

Two loops share a

2\,\Omega

resistor between points A and B. The left loop has a

12\,\text{V}

battery (positive at A) and a

4\,\Omega

resistor. The right loop also has a

12\,\text{V}

battery but with its positive terminal at B (opposite orientation) and another

4\,\Omega

resistor. Clockwise currents in the left and right loops are

I_1

and

I_2

respectively. Determine the magnitude and direction of the current through the

2\,\Omega

resistor.