A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by 
T in a time t. A number N of similar cells is now connected in series with a wire of the same material and cross–section but of length 2 L. 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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$As, R = \frac{\rho L}{A} ; R_1 = \frac{\rho 2L}{A} = 2R m = ALd ; m_1 = 2ALd = 2m where d is density. Now, \frac{(3V)^2 t}{R} = mc \Delta T \ldots (i) and \frac{(NV)^2 t}{2R} = 2mc \Delta T \ldots (ii) Solving Eqs. (i) and (ii), we get N = 6$
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