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 $2L$. 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)

$6$

Let $R$ and $m$ be the resistance and mass of the first wire, then the second wire has resistance $2R$ and mass $2m$.

Let $E$=emf of each cell, $S=$ specific heat capacity of the material of the wire.

For the first wire, current $i_1=\frac{3E}{R}$ and ${i_1}^{2}RT=mS\Delta T$

For the second wire, $i_2=\frac{NE}{2R}$ and ${i_2}^2\left(2R\right)t=2mS\Delta T$.

Thus, $i_1=i_2$ or $N=6$.