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 `DeltaT` 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 `DeltaT` in the same time t. the value of N is

Options

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

Answer

B

Explanation

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