Two conducting wires of the same material and of equal lengths and equal diameters are first connected in parallel and then in series in a circuit across the same potential difference. The ratio of heat produced in parallel and series combinations is
- A.2:1
- B.4:1
- C.1:2
- D.1:4
Correct answer
Explanation
The correct answer is B, 4:1. With the same voltage, heat varies inversely as resistance, and the parallel resistance is one-fourth of the series resistance.
The two wires are identical, so each has the same resistance R. In series the total resistance is R + R = 2R; in parallel it is R/2. For a fixed potential difference V, the heat produced in time t is H = V²t/R. So the heat in parallel is V²t ÷ (R/2) = 2V²t/R, and in series it is V²t ÷ 2R = V²t/2R. Dividing the two gives 4:1. This is why household appliances are connected in parallel: each gets the full mains voltage and works at its rated power.
A is wrong because 2:1 would follow if the resistances differed by a factor of two, not four. C is wrong because it reverses the ratio and also uses the wrong factor. D is wrong because it reverses the correct ratio; the parallel combination produces more heat.
Exam tip: at fixed V, H = V²t/R; identical resistors: series 2R, parallel R/2, so heat ratio parallel to series = 4:1.
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