Question

A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by T 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 2 L. The temperature of the wire is raised by the same amount T in the same time t. the value of N is

• A. 4
• B. 6
• C. 8
• D. 9

Answer 1

The correct option is B 6

Let R and m be the resistance and mass of the first wire, then the second has resistance 2R and mass 2m. Let E=emf of each cell,S=specific heat capacity of the material of the wire. For the first wire, current $i_1=\frac{3E}{R}$ and $t_1^{2}Rt=mS△T$
for the second wire, $i_2=\frac{NE}{2R}$ and $t_2^2\left(2R\right)t=2mS△T$. Thus, $i_1=i_2$ or N=6.