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

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

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).

State the ideal transformer voltage and current ratios. [2 marks]

A step-down transformer has $N_p = 5000$, $N_s = 250$. With $V_p = 11000 \text{ V}$ and secondary delivering $20 \text{ A}$, calculate $V_s$, $I_p$ and the transferred power. [4 marks]

A Townsville Powerlink line delivers $300 \text{ MW}$ at $275 \text{ kV}$ over $25 \text{ ohms}$. (a) Calculate the line current and the $I^2 R$ loss. (b) Compare with the same power at $33 \text{ kV}$ on the same line.