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 is raised by $\Delta T$ 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 $4\,L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time. The value of $N$ is

• A. 4
• B. 6
• C. 8
• D. 9

Answer 1

Answer: (B)

$In \, the \, first \, case \frac{(3E)^2}{R}t = ms\, \Delta T \, \, \, \, \, \, \, \, \, \, \, ...(i) $
$\, \, \, \, \, \, \, \, \bigg[ H=\frac{V^2}{R}t \bigg]$
When length of the wire is doubled, resistance and mass both are doubled.
Therefore, in the second case.
$\frac{(NE)^2}{2R} . t = (2m)s \Delta T \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, ...(ii)$
Dividing Eq. (ii) by (i), we get
$\frac{N^2}{18} = 2 \, or \, N^2 = 36 \, or \, N = 6$