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`

Answer

B

Explanation

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