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 $4L$. 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)

$Inthefirstcase\frac{(3E{)}^2}{R}t=ms\Delta T...(i)$
$[H=\frac{V^2}{R}t]$
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
$\frac{N^2}{18}=2or{N}^2=36orN=6$