9702/Oct Nov/13/2017/Q36

Two cells, each with electromotive force (e.m.f.) E, but different internal resistances r1 and r2, are
connected in series to a resistor R. The reading on the voltmeter is 0 V.

What is the resistance of R?

Solution:
Answer: B


Total e.m.f = E+E = 2E

Total resistance = r1 + r2 + R

Current, i = (2E)/ (r1+r2+R) ------------------(i)

P.D. across 1st cell

V = E - ir1

0 = E - ir1

This implies,

i = E/r1 ------------------(ii)

From (i) and (ii), we have

=> r1 + r2 + R = 2r1

R = r1 - r2

Reference: PYQ - Oct/Nov 2017 Paper 13 Q36