AS Daily A Level Physics question
Two identical 12 V, 6 W bicycle lamps are designed to run from a 12 V battery when wired in parallel. By mistake, the lamps are wired in series across the same ideal 12 V battery. Treat each lamp as an ohmic resistor set by its rating. Which statement must be true about the power in each lamp in the series connection, compared with the correct parallel connection?
Answer
The correct answer is B.
Correct: B — About 1.5 W in each lamp — one quarter of the correct power. A 12 V, 6 W rating implies each lamp has R ≈ V^2/P = 144/6 = 24 Ω. In parallel, each gets 12 V and 6 W. In series across 12 V, total R = 48 Ω, so I = 12/48 = 0.25 A and each lamp has about 6 V across it; power per lamp ≈ VI = 6 × 0.25 = 1.5 W, i.e. a quarter. A misapplies the idea that current halves but misses that voltage per lamp also halves, giving quarter power, not half. B is correct as shown by the calculation. C ignores that series wiring splits the supply voltage, reducing power. D reverses the effect; with lower current and voltage per lamp in series, power cannot increase.