A 110 V d.c. supply is connected to a heater, a fuse and a switch, as shown. Owing to a fault in the system, power is not supplied to the heater. A technician diagnoses the fault using a voltmeter.

Question 8

A 110 V d.c. supply is connected to a heater, a fuse and a switch, as shown.

Owing to a fault in the system, power is not supplied to the heater. A technician diagnoses the fault using a voltmeter.

He closes the switch and connects his meter between the positive supply terminal S+ and the fuse terminal F2. The voltmeter reads 110 V.

Which diagnosis is correct?

A The fuse has melted.

B The fuse has not melted and there is a short circuit in the heater.

C The fuse has not melted and there is no path for current through the heater.

D The fuse has not melted and the switch has operated correctly.

Reference: Past Exam Paper – November 2015 Paper 11 Q35

Solution:

Answer: A. 

The purpose of a fuse is usually to prevent a too great current to flow in a circuit. When the current is less, we can consider the fuse to act as a connecting wire, with no p.d. across it.

Normally, when a fuse has not melted, there would be no potential difference (p.d.) across it. That is, the terminal F2 would also be at a potential of 110 V (like the positive terminal of the supply) such that the p.d. = 110 – 110 – 0 V.

[B, C and D are incorrect as the question says that the voltmeter reads 110 V].

The voltmeter reads 110 V. This means that terminal F2 is at a potential of 0 V such that the p.d. is 110 – 0 = 110 V (as read by the voltmeter). This indicates that the full potential difference of the supply is across the fuse. There is no p.d. across the other components in the circuit. This indicates that current is not flowing. So, the fuse must have melted.

Terminal F2 may be considered to be connected directly to the other terminal of the supply (as there is no p.d. across the other components) and thus, is at a potential of 0 V. This is why the p.d. between the positive terminal of the supply and F2 is 110 V.