Question

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

• A. 4
• B. 6
• C. 8
• D. 9

Answer 1

Answer: (B)

As, $R=\frac{\rho L}{A} ; R_{1}=\frac{\rho 2 L}{A}=2 R$
$m=A L d ;\, m_{1}=A 2 L d=2 m$
where $d$ is density.
Now, $\frac{(3 V)^{2} t}{R}=m c \Delta T$ ...(i)
and $\frac{(N V)^{2} t}{2 R}=2 m c \Delta T$ ...(ii)
Solving Eqs. (i) and (ii), we get $N=6$