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AS Daily A Level Physics question

2026-03-06 OCR A High level GCSE electricity Module 4.2.1 Charge and current Module 4.2.2 Energy, power and potential difference Module 4.2.3 Resistance; series and parallel circuits

An ideal 9 V battery is connected to resistor A (6 Ω) in series with a junction. One branch has resistor B (6 Ω). The other branch has a switch S in series with resistor C (12 Ω). Initially S is open so only B is connected. When S is closed, C is added in parallel with B. Assume all resistors are ohmic and their values do not change with temperature. Which statement must be true about the power dissipated in resistor A when S is closed, compared with when S is open?

  1. A Increases by about 20%, because the total resistance falls from 12 Ω to 10 Ω so the current rises by 20%, and power in A follows the current.
  2. B Decreases by about 17%, because the new branch diverts current away from A, reducing its power.
  3. C No significant change, because A’s resistance is unchanged and it is before the junction.
  4. D Increases by about 44%, because the added parallel path lowers total resistance so the series current rises by 20%, and power in A varies with the square of current. (correct)

Answer

The correct answer is D.

Correct: D — Increases by about 44%, because the added parallel path lowers total resistance so the series current rises by 20%, and power in A varies with the square of current. With S open: total resistance = 6 Ω + 6 Ω = 12 Ω, so current = 9/12 = 0.75 A; with S closed: parallel(6 Ω, 12 Ω) = 4 Ω, total = 6 Ω + 4 Ω = 10 Ω, so current = 9/10 = 0.90 A (20% higher); power in A ∝ I^2, so the factor is (0.90/0.75)^2 = 1.44 → a 44% increase. A misinterprets power as merely proportional to current, missing the square dependence, hence only 20%. B assumes current is diverted from A; but A is in series and carries the total current, which actually increases, so the sign is wrong (and the 17% comes from a mistaken linear drop idea). C assumes being before the junction fixes the power; however the series current through A changes when the circuit’s total resistance changes. D matches the correct 44% increase from the I^2 dependence and the computed current change.

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