Quick questions on Transformers and AC power transmission (QCE Physics Unit 3)

A transformer is two coils (the primary and the secondary) wound on the same ferromagnetic core. An alternating current in the primary produces an alternating flux in the core. The same changing flux links the secondary, inducing an EMF in it (Faraday's law).

An ideal transformer has no losses. Power in equals power out:

Faraday's law requires $d\Phi / dt \neq 0$ to induce a secondary EMF. A steady DC primary current produces a constant flux, so the secondary EMF is zero (except during the brief switch-on transient). AC, by reversing direction many times per second, produces the continuous flux change required.

Typical efficiencies: about 95 percent for small transformers, above 99 percent for large grid transformers.

Transmitting electrical power $P = V I$ over a long line of resistance $R_{\text{line}}$ wastes power as:

A power station delivers $1.0$ MW to a town through a transmission line of total resistance $5.0$ ohms. Compare the line losses at $1000$ V transmission versus $100$ kV transmission.

Expect a transformer characteristics table (turns counts, voltage and current measurements) with questions on the inferred turns ratio, the deviation from the ideal model, and the energy dissipated in the windings. Alternatively, a transmission-line stimulus with two transmission voltages and a question on the $I^2 R$ losses.

A standard IA2 design measures secondary voltage against primary voltage (or against $N_s / N_p$) using a low-voltage AC supply and a hand-wound transformer. Strong reports linearise $V_s$ against $V_p$ for fixed turns ratio (slope $= N_s / N_p$) and discuss systematic deviations from the ideal model (flux leakage at low turns counts, $I^2 R$ heating at high primary currents).

$V_s / V_p = N_s / N_p$, but $I_p / I_s = N_s / N_p$. The voltage and current ratios are inverses of each other.

A common error in design questions; the device gives no output (no induced EMF) and may overheat. Always state the AC requirement when explaining transformer operation.

Eddy-current losses and hysteresis losses are both in the core; resistive losses are in the windings; flux leakage is a geometry issue. Markers expect you to distinguish them.

It is to reduce $I^2 R$ loss, which depends on $I^2$, not on $V$. Higher $V$ at the same $P$ means lower $I$ and quadratically smaller losses.

A step-up transformer increases voltage at the cost of decreasing current; total power is conserved (or reduced slightly by losses in a real transformer).

The primary is whichever coil is connected to the source; the secondary is whichever is connected to the load. A step-up transformer used backwards becomes a step-down transformer.