AS Daily A Level Physics question
In a lab check of heating, two fixed resistors labelled R and 2R are tested with the same 9 V battery. Test 1: they are connected in series for one minute. Test 2: they are reconnected in parallel, each directly across the battery, for one minute. Assume their resistances do not change with temperature, and “hotter” means the one dissipating more electrical power in that test. Which statement must be true?
Answer
The correct answer is C.
Correct: C — Series: 2R hotter; Parallel: R hotter; In parallel, power in R is twice that in 2R. In series the same current flows through both, so the larger resistance dissipates more power (proportional to R), but in parallel both have the same voltage, so the smaller resistance dissipates more power (proportional to 1/R), giving PR:P2R = (V^2/R):(V^2/2R) = 2:1. A The claim of equal power in parallel ignores that equal voltage in parallel means the smaller resistance takes more power, not equal. B In series the same current does not make the powers equal; power scales with R, and in parallel the larger resistance does not take more power. C This matches the series-versus-parallel constraints and gives the correct 2:1 power ratio in parallel. D It gets series wrong (the smaller resistor is not hotter with the same current) and reverses the parallel power ratio.