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 at $△T$ in time $t$. $N$ number 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 $△T$ in the same time $t$. The value of $N$ is:

• A. 4
• B. 6
• C. 8
• D. 9

Answer 1

Answer: (B)

6

We know,

$\left(\frac{V^2}{R}\right)=m\Delta T$

where variables have their usual meanings.

For given data, $V^2=Rm$

Now,

$\left(3V^2\right)\propto Rm$

$\left(N{V}^2\right)\propto \left(2R\right)\left(2m\right)$

From above equations we can write,

$\frac{N^2}{9}=4$

$\therefore N^2=36$

$\therefore N=6$