Explain the operation of AC and DC generators using electromagnetic induction

What this dot point is asking

WACE wants you to explain how a generator converts mechanical rotation into electrical energy, and to distinguish AC from DC output by the connection hardware. This is the practical inverse of the motor effect: instead of current producing motion, motion produces current.

Inducing the emf

As a coil of $N$ turns and area $A$ rotates at angular speed $\omega$ in a field $B$, the flux is $\Phi=BA\cos(\omega t)$, so by Faraday's law the induced emf is

The emf varies sinusoidally with a peak value $\varepsilon_0=NBA\omega$. It is maximum when the coil plane is parallel to the field (flux changing fastest) and zero when the plane is perpendicular (flux momentarily at its peak and not changing).

The AC generator

In an AC generator the coil ends connect to two slip rings, each in continuous contact with a brush. The connection never swaps, so as the coil rotates the output reverses direction every half turn, tracing a full sine wave each revolution. This is how mains electricity is produced in power stations.

The DC generator

A DC generator replaces the slip rings with a single split-ring commutator. Each half turn, as the emf in the coil would reverse, the commutator swaps which half of the ring touches which brush. The external connection therefore always sees the same polarity, so the output is a series of positive humps, never going negative. It is direct current, though it pulses rather than being perfectly steady.

Controlling the output

The peak emf $\varepsilon_0=NBA\omega$ shows four ways to increase the output: more turns $N$, a stronger field $B$, a larger coil area $A$, or faster rotation $\omega$. Faster rotation also increases the frequency of the AC, since one cycle is produced per revolution.

Explaining the difference clearly

When asked to contrast AC and DC generators, the load-bearing point is the connection hardware: slip rings give AC, a split-ring commutator gives DC. The coil and field are otherwise identical. Mention that the commutator reverses the external connection just as the coil emf would reverse, which is why the DC output stays one-way.