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` and `m` the resistance and mass of the first wire, then the second wire has resistance `2R` and mass `2 m`. Let `E =` emf of each cell, `S =` specific heat capacity of the material of the wire. For the first wire, current `i_(1) = (3 E)/(R )` and `i_(2) = (NE)/(2R) = mS Delta T`
For the second wire, `i_(2) = (NE)/(2R)` and `i_(2)^(2) (2 R) t = 2 m S Delta T`.
Thus, `i_(1) = i_(2)` or `N = 6`.