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

(b) Let R be the resistance of wire.

Energy released in t seconds `= (3V)^2 /R xx t`
`Q = (9V^2)/R xx t`
`:. mcDeltaT = (9v^2)/R xx t (.: But Q = mcDeltaT)`……(i)
Let R' be the resistance of the second wire

`R' = 2R (.: length is twice)`
`:. Energy released in t-seconds = (NV)^2/(2R) xx t`
Also `Q' = m'cDeltaT = (2m)CDeltaT`
`2mcDeltaT = (N^2V^2)/(2R) xx t `
Dividing (i) by (ii)
`(mcDeltaT)/(2mcDeltaT) = (9V^2 xx t//R)/(N^2V^2 t//2R) or, 1/2 = (9xx2)/N^2`
or `N^2 = 18 xx 2 :. N = 6`.