A.C. generator

An a.c. generator produces an alternating e.m.f. by rotating a coil and a magnetic field relative to each other. This rotation changes the magnetic field passing through the coil, inducing an e.m.f. across it.

The induced e.m.f. reverses direction every half-turn. If the coil is connected to a complete external circuit, the current also reverses direction, producing an alternating current.

A.C. generator designs

In a rotating-coil generator, the coil turns between stationary magnetic poles. Each end of the coil connects to a separate slip ring, and the rings turn with the coil. Stationary brushes press against the rings, maintaining an electrical connection to the external circuit while the coil rotates.

Alternatively, a magnet can rotate near a stationary coil. The magnetic field through the coil then changes as the magnet turns, inducing an alternating e.m.f. Because the coil does not rotate, it can be connected directly to the external circuit without slip rings.

A.C. generator e.m.f.–time graphs

When a coil rotates at constant speed in a uniform magnetic field, its induced e.m.f. changes continuously in magnitude and reverses direction every half-turn. A graph of e.m.f. against time has a sinusoidal shape: its positive and negative parts represent e.m.f.s in opposite directions.

One complete cycle of the graph corresponds to one full rotation of the coil. Since the coil rotates at constant speed, equal fractions of a rotation take equal fractions of a cycle’s time.

Coil position and the e.m.f. graph

The e.m.f. depends on how quickly the magnetic field through the coil changes as it turns:

• When the plane of the coil is perpendicular to the magnetic field, the field through the coil is momentarily changing least. The induced e.m.f. is zero.
• When the plane of the coil is parallel to the magnetic field, the field through the coil is changing most rapidly. The induced e.m.f. has its maximum magnitude: it is at either a positive peak or a negative trough.

Starting from a zero-e.m.f. position, the coil reaches a maximum-magnitude position after a quarter-turn, another zero after a half-turn, and the opposite maximum after three-quarters of a turn. After one full turn, it returns to the original zero-e.m.f. position.

Successive zeros are therefore half a turn apart. A peak and the next trough are also half a turn apart, but they represent opposite e.m.f. directions. Successive peaks are one full turn apart.

Choosing the start of the graph

The shape of a sketched graph depends on where the coil starts and which e.m.f. direction is labelled positive. For example, if the coil starts with its plane perpendicular to the field, the graph starts at zero; it may then rise or fall depending on the chosen positive direction. If the coil starts parallel to the field, the graph starts at a peak or trough.