In order to measure the rms value of an alternating current in a cable, a small coil of wire is placed close to the cable.

The plane of the small coil is parallel to the direction of the cable. The ends of the small coil are connected to a high resistance ac voltmeter.

Use Faraday’s law to explain why an emf is induced in the small coil.

The graph below shows the variation with time \(t\) of the current in the cable.

On the axes below, draw a sketch graph to show the variation with time of the emf induced in the small coil.

Explain how readings on the high resistance ac voltmeter can be used to compare the rms values of alternating currents in different cables.

induced emf is (directly) proportional/equal to rate of change/cutting of flux (linkage);

current produces a (time changing) magnetic field;

field changes with time;

which produces a time changing flux in the coil;

or

same frequency as current graph;

\( \pm 90° \) phase shift;

if the coil position/orientation relative to the cables is the same in all measurements;

if the coil distance from the cables is the same in all measurements;

the voltage measured across the coil is proportional to current in the cable;

The chain of argument needed to be clear in answers. A correct statement of Faraday‟s Law should lead to the recognition that the current produces a magnetic field, that this field is changing, and that therefore a time changing flux exists inside the coil.

Candidates could identify the similarity of frequency between graphs but the phase relationship usually defeated them.

Candidates failed to rise to the challenge of this question or indeed to read it correctly. They were asked to explain how the voltmeter can be used to compare the values of currents in different cables. This involves making both the distance from the centre of the cable and the orientation common to both sets of measurements. It also involves the recognition by the candidate that the current is directly proportional to the reading on the voltmeter.