9702/Oct Nov/13/2017/Q37

Three identical cells each have electromotive force (e.m.f.) E and negligible internal resistance.
The cells are connected to three identical resistors, each of resistance R, as shown.

What is the potential difference between P and Q?

Solution:

Answer: C

Two of the cells are providing an e.m.f. in one direction and the other in the opposite direction. So,

Overall e.m.f. = E + E – E = E

The resistors are connected in series.

Total resistance = R + R + R = 3R

From Ohm’s law, I = V / R

Current in circuit = overall e.m.f. / total resistance = E / 3R

Consider the potentials in the section PQ.

Let P be at a potential of E.

The e.m.f. of the cell is E. That is, the potential difference between the terminals of the cell is E. If point P is at a potential of 0, then the point between the positive terminal of the battery and the resistor is E.

Current in the circuit = E / 3R

p.d. V across a resistor = IR = (E/3R) × R = E / 3

Thus, potential at point Q = E – E/3 = 2E / 3

In another wording, potential difference between 2 points means the ‘difference in potential’ between the 2 points.

p.d. between P and Q = potential at Q – potential at P

p.d. between P and Q = (2E / 3) – 0 = 2E / 3

Reference: PYQ - Oct/Nov 2017 Paper 13 Q37