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

`R = (rho L)/A, R_(1) = (rho(2L))/A = 2R`
Density `= m/v rArr d = m/(AL)`
`therefore m =Ald, m_(1) = A2Ld = 2m`
`H_(1) = (3E)^(2)/R t = ms Deltat`…….. (i)
`H_(2) = (ne)^(2)/(2R) xx t = 2msDeltaT`……. (ii)
By (i) and (ii) N = 6