A wire of length L and 3 identical cells of negligible internal resistance are connected in series. Due to the current, the temperature of the wire is raised by `Delta 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 2L. The temperature of the wire is raised by the same amount`Delta t` in the same time t. The value of N is

Explanation

In the first case `((3E)^(2))/(r).t=ms DeltaT" ….(1)"`
`[H=(V^(2))/(r).t]` When length of the wire is doubled, resistance and mass both are doubled
Therefore, in the second case,
`((NE)^(2))/(2R).t=(2m)sDeltaT" ……..(2)"`
Dividing Eq. (2) by Eq. (1)
we get `(N^(2))/(18)=2 or N^(2)=36 or N=6`