# Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel

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Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be –

(a) 1:2 (b) 2:1 (c) 1:4 (d) 4:1

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Heat produced in the circuit is inversely proportional to the resistance R. Let RS and RP be the equivalent resistances of the wires if connected in series and parallel respectively. Let R be the resistance of each wire. If the resistors are connected in parallel, the net resistance is given by

Therefore, the ratio of heat produced in series and parallel combinations is 1:4. Hence, the option (c) is correct.