A2 Daily A Level Physics question
A generator must deliver 12 kW to a remote workshop via overhead lines whose total resistance is 3.2 Ω. In setup B, an ideal transformer arrangement makes the line voltage 2.4 kV. In setup A, the step-up is doubled so the line voltage is 4.8 kV, while the workshop still receives 12 kW at the same local voltage as before (both transformers ideal; ignore core/winding losses). Compared with setup B, which statement must be true for setup A?
Answer
The correct answer is D.
Correct: D — The line current halves and the line heating loss is one quarter. For the same transmitted power, doubling the line voltage halves the line current; heating in the fixed-resistance line scales with the square of current, so the loss falls by a factor of four. This also matches the limiting case: very large step-up gives very small current and negligible line loss. A The current cannot be unchanged: for fixed power, raising line voltage reduces current; even if current did halve, the loss would drop to a quarter, not a half. B Halving the current is right, but heating does not halve; it becomes one quarter because it depends on current squared. C Halving current is correct, but claiming doubled loss confuses the role of voltage in the line; with fixed resistance, heating is set by current, so reduced current reduces heating, not increases it.