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Ten identical cells connected in series are needed to heat a wire of length one meter and radius ‘r’ by 10°C in time ‘T’. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time ‘T’?

1. 10
2. 20
3. 30
4. 40

Correct answer: 20

Solution

The heat generated is proportional to the resistance of the wire and the square of the current. Resistance is proportional to the length of the wire. Doubling the length doubles the resistance, so to maintain the same heating in the same time, the voltage (and hence the number of cells) must also double. Thus, 20 cells are required.

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