Physics - Current Electricity Question with Solution | TestHub

By Ohm's law, $V=IR$.

Let the current and resistance at $0^{\circ }\mathrm{C}$ be $i_0\&R_0$ respectively.

Let the current and resistance at $100^{\circ }\mathrm{C}$ be $i_{100}\&R_{100}$ respectively. By the given condition,

$$\begin{gathered} i_0{R}_0=i_{100}{R}_{100} \\ \Rightarrow 2R_0=1.2R_0(1+100\alpha ) \\ \Rightarrow 1+100\alpha =\frac{5}{3} \\ \Rightarrow 50\alpha =\frac{1}{3} \end{gathered}$$Since the voltage remains constant,

$$\begin{gathered} i_{50}{R}_{50}=i_0{R}_0 \\ \Rightarrow i_{50}=\frac{i_0{R}_0}{R_{50}}=\frac{2\times R_0}{R_0\left(1+50\alpha \right)}=\frac{2}{1+\frac{1}{3}}=1.5\text{A} \\ \Rightarrow i_{50}=15\times 10^2\text{mA} \end{gathered}$$