Between junctions X and Y is a resistor shared by two adjacent loops

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

Between junctions X and Y is a

3\,\Omega

resistor shared by two adjacent loops. The left loop contains a

9\,\text{V}

battery (positive at X) and a

3\,\Omega

resistor. The right loop contains a

15\,\text{V}

battery (positive at Y) and a

6\,\Omega

resistor. Clockwise loop currents are

I_1

(left) and

I_2

(right). (a) Find

I_1

and

I_2

. (b) Hence calculate the power supplied by each battery.