$A$ 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 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 $\Delta T$ in the same time $t$. The value of $N$ is :
Medium
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In the first case,
$\frac{(3 E)^{2}}{R} t=(m) s \Delta T$$.......................(i)$
When the length of the wire is doubled, resistance and mass both are doubled. Therefore, in the second case
$\frac{(N E)^{2}}{2 R} t=(2 m) s \Delta T$
Dividing Eq. $(ii)$ by Eq. $( i ),$ we get $N=6$
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