Q 12-03-284JEE MainJEE Main 2018 (16 Apr, Shift 1)Easy
A heating element has a resistance of $100\ \Omega$ at room temperature. When it is connected to a supply of $220\ \text{V}$, a steady current of $2\ \text{A}$ passes in it and temperature is $500^\circ\text{C}$ more than the room temperature. The temperature coefficient of resistance of the heating element is
Answer: (B) $2\times10^{-4}\ ^\circ\text{C}^{-1}$
Hot resistance: $R = \dfrac{220}{2} = 110\ \Omega$.
$$R = R_0(1 + \alpha\Delta T) \;\Rightarrow\; 110 = 100(1 + 500\alpha) \;\Rightarrow\; \alpha = \frac{0.1}{500} = 2\times10^{-4}\ ^\circ\text{C}^{-1}$$
Solution by Sreeraj P, M.Sc Physics