Quick questions on Generators, transformers and AC power transmission: VCE Physics Unit 3

A generator is a coil rotated in a magnetic field. By Faraday's law, the changing flux through the coil induces an EMF. If the coil has $N$ turns, area $A$, in field $B$, rotating at angular frequency $\omega$:

A sinusoidal AC voltage swings between $+V_{peak}$ and $-V_{peak}$. The average voltage over a cycle is zero, which is unhelpful for calculating power. Instead we use the root-mean-square (RMS) value:

A transformer is two coils wound around a common iron core. AC in the primary coil produces a changing magnetic flux in the core. The same changing flux passes through the secondary coil, inducing an EMF.

The power lost as heat in transmission lines of resistance $R$ depends on the current squared:

The transmission cables form a voltage divider with the load. Voltage delivered to the load:

Uses slip rings: a continuous ring on each end of the coil, with brushes feeding the external circuit. As the coil rotates, the current reverses every half-turn. The external circuit sees alternating current.

Uses a split-ring commutator (the same device as in a DC motor). It swaps the brush connections every half-turn, so the external current always flows in the same direction. The output is a series of half-wave humps; with many coils at different angles, the output approaches a smooth DC voltage.

Slip rings (continuous) give AC. A split-ring commutator (two halves) gives DC.

$P = V I$ uses RMS values. Using peak values overestimates power by a factor of 2.

Transformers need a changing flux. Constant DC produces no induced EMF in the secondary.

When voltage steps up, current steps down (energy is conserved). $V_1 / V_2 = I_2 / I_1$.

$P_{loss} = I^2 R$ uses the cable current and cable resistance, not the transmitted voltage. The transmitted voltage drops mostly across the load, not the cables.