Two loops share a resistor

PHYSICS · Single correct · CBSE · Physics · Current Electricity · Current Electricity

Problem

Two loops share a

5\,\Omega

resistor. The left loop contains a

15\,\text{V}

battery and a

10\,\Omega

resistor. The right loop contains an unknown battery

\mathcal E_{x}

and a

20\,\Omega

resistor. Neglect the resistance of the connecting wires. If the current through the shared

5\,\Omega

resistor is zero, what is the value of

\mathcal E_{x}

? (a)

25\,\text{V}

(b)

15\,\text{V}

(c)

30\,\text{V}

(d)

37.5\,\text{V}