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

Options

A. 4
B. 6
C. 8
D. 9

Explanation

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