Physics - Current Electricity Question with Solution | TestHub

By Ohm's law, $V=IR$.

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

Let the current and resistance at $100 °\mathrm{C}$ 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,

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