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A wire of length L and three identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by $∆$ T in a time t. N number of similar cells are now connected in series with a wire of the same material and cross-section but of length 2L.
The temperature of the wire is raised by the same amount $∆$ T in the same time t. The value of ‘N’ is

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answer is B.

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Detailed Solution

$Energy = \frac{(3 V)^{2} t}{R}$

$Q = \frac{9 V^{2} t}{R} = mc ΔT \to (1)$
$m \propto l \propto R$
$Q^{1} = m^{1} cΔT = 2 mCΔT = \frac{N^{2} V^{2}}{2 R} t \to (2)$

$\frac{(1)}{(2)}; \frac{mcΔT}{2 mcΔT} = \frac{9 v^{2} \times t / R}{N^{2} v^{2} t / 2 R}; N = 6$

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