Question 5
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?
A
0 B
3E
C
2E
/ 3 D
E
Reference: Past Exam Paper – November 2017 Paper 13 Q37
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
/ R – 0 = 2E / R
