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 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. The value of N is

• A. 4
• B. 6
• C. 8
• D. 9

Answer 1

The correct option is B 6

Heat $=mS\Delta T=i^{2}Rt$
Case I: Length (L) $\Rightarrow$ Resistance = R and mass = m
Case II: Length (2L) $\Rightarrow$ Resistance = 2R and mass = 2m
So $\frac{m_1{S}_1\Delta T_1}{m_2{S}_2\Delta T_2}=\frac{i_1^2{R}_1{t}_1}{i_2^2{R}_2{t}_2}\Rightarrow \frac{mS\Delta T}{2mS\Delta T}=\frac{i_1^{2}Rt}{i_2^{2}2Rt}\Rightarrow i_1=i_2\Rightarrow \frac{\left(3E\right)}{R}=\frac{\left(NE\right)}{2R}\Rightarrow N=6$