In the circuit shown, the ammeter reading is zero. What is the resistance of resistor R?

Question 27

In the circuit shown, the ammeter reading is zero.

What is the resistance of resistor R?

A 100 Ω                       B 200 Ω                       C 400 Ω                       D 600 Ω

Reference: Past Exam Paper – November 2018 Paper 13 Q37

Solution:

Answer: C.

Let the negative terminals of the cells be at 0 V and the upper terminals of the cells to at their respective e.m.f.s.

For the ammeter reading to be zero, the potential difference between the 2 terminals of the ammeter should be zero. That is, both terminals of the ammeter should be at the same potential.

Note that the lower junction being at 0 V is just an assumption here and may not always be true, especially since we have 2 different cells of different e.m.f.s. In this case, the potentials at the middle junctions should also be zero for the ammeter reading to be zero. That is, there should be no potential difference between the 2 middle junctions.

Consider the left section.

We can use the potential divider equation to determine the p.d. across the resistors.

p.d. across 100 Ω = [100 / (100+50)] × 12 = 8 V

Since the lower junction is at 0 V, the middle junction on the left will be at 8 V.

For the ammeter reading to be zero, the potential at the middle junction on the right should also be at 8 V.

Consider the right section.

p.d. across the 200 Ω = 8 V

p.d. across the 200 Ω = [200 / (200+R)] × 24

[200 / (200+R)] × 24 = 8

200 × 24 = 8 × (200+R)

200 + R = (200×24) / 8

200 + R = 600

R = 600 – 200 = 400 Ω

 

Many would choose answer A, which assumes the same ratio across each pair of resistors that are facing each other in the two circuits. This is not correct because the two cells have different e.m.f.s.