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A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by Δ T in a time t . N number 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 Δ T in the same time. The value of N is

Correct answer

6

Step-by-step solution

In the first case, 3 E 2 R t = m s Δ T ...(i) H = V 2 R t When length of the wire is doubled, resistance and mass both are doubled. Therefore, in the second case, N E 2 2 R · t = 2 m s Δ T ...(ii) Dividing equation (ii) by (i), we get N 2 18 = 2 or N 2 = 36 or N = 6 .

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