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Electrical Power & Heating Effect question from NEET 2013

Q53NEET 2013Difficult

Electrical Power & Heating Effect

Ten identical cells connected in series are needed to heat a wire of length one meter and radius 'r' by 10oC 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'?

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Answer: (a)

Doubling the length doubles both $R$ and the mass, so heat needed doubles: $H' = 2H$ .
$H = \frac{V^2t}{R}$ : $\frac{V'^2}{2R} = 2\frac{V^2}{R} \Rightarrow V' = 2V$ .
Voltage doubles, so cells needed $= 2 \times 10 = 20$ . So the answer is (a).

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