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

Answer

6

Explanation

In the first case,
`(3E)^(2)/R t = msDeltat`…….. (ii)
When the length of the wire is doubled, resistance and mass both are doubled. Therefore, in the second case,
`(NE)^(2)/(2R)t = (2m)s DeltaT`…........ (ii)
Dividing Eq.(ii) by (i) we get,
`N^(2)/18 = 2`
or `N^(2) = 36`
or N = 6