Question

A wire of length $L$ and 3 identical resistors of the same resistance as the wire 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 resistors are 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

Answer 1

Let resistance of resistors and wire be $R$, mass of the wire be $m$ and the specific heat of the material of the wire be $S$

For wire of length $L$,
Heat $=i^2(R+3R)t=mS\Delta T$ ...(1)

For wire of length $2L$,
Heat $=i^2(2R+NR)t=2mS\Delta T$ ...(2)

Divide eq. (1) and (2)
$N=6$