Question

A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to this 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 wire is raised by same amount $\Delta T$ in the same time $t$. Find the value of $N$.

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is C $6$

Since we have
$\text{Heat}=mS\Delta T=i^{2}Rt$
CASE-1: Length $\left(L\right)$,Resistance $R$ and mass $m$
CASE-2: Length $\left(2L\right)$, Resistance $2R$ and mass $2m$
$\Rightarrow \frac{m_1{S}_1\Delta T_1}{m_2{S}_2\Delta T_2}=\frac{i_1^2{R}_1{t}_1}{i_2^2{R}_2{t}_2}$
$\Rightarrow \frac{mS\Delta T}{2mS\Delta T}=\frac{i_1^{2}Rt}{i_2^{2}2Rt}$
$\Rightarrow i_1=i_2\Rightarrow \frac{3E}{R}=\frac{NE}{2R}\Rightarrow N=6$