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An electric kettle's heating element is a single wire of length L and diameter d, and it takes 4 minutes to heat 0.5 kg of water by 40 K. The element is then replaced by two wires of the same material, each of length L and diameter 2d. For the same temperature rise of the same water, how long does it take? [JEE Advanced 2014]

1. 4 if wires are in parallel
2. 2 if wires are in series
3. 1 if wires are in series
4. 0.5 if wires are in parallel

Correct answer: 2 if wires are in series

Solution

Each new wire has R/4; in series the total is R/2, doubling the power and halving the time to 2 minutes.

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