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. 3
B. 2
C. 6
D. 4

Answer

C

Explanation

In the first case, three identical cells are connected in series with a wire of length L. let the terminal potential difference of each cell is V and resistance of the wire is R. Then heat developed in the wire in time t is
`H=((3V)^(2))/(R)t=msDeltaT`
where m is the mass of the wire, s-the specific heat of its material and `DeltaT` is the rise in its temperature. When N such identical cells are connected in series, the effective terminal otential is NV volt ad if the length of the wire is doubled, its resistance and mass also doubled. Then heat develope in the wire is
`H=((NV)^(2))/(2R)t=(2m)s.DeltaT`
DIviding both the equations, we get
`(N^(2))/(2xx9)=2impliesN=6`