A metal coil has a resistance of 20 Ω at 20 °C. The temperature coefficient of resistivity of the metal is \(4\times10^{-3}\ ^\circ\mathrm{C}^{-1}\). Ignore any change in the size of the coil. The resistance of the coil at 70 °C is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24 Ω
The size of the coil does not change. So its resistance changes with temperature in the same way as its resistivity, \( R_T=R_0[1+\alpha(T-T_0)] \). Here \( \alpha \) tells how much the resistivity changes for each 1 °C rise in temperature.
\( \begin{aligned} R_{70} &= R_{20}[1+\alpha(T-T_0)] \\ &= 20[1+4\times10^{-3}\times(70-20)] \\ &= 20\times1.2 \\ &= 24\ \Omega \end{aligned} \)
NCERT (2026-27):
Temperature Dependence of Resistivity – “… Over a limited range of temperatures, that is not too large, the resistivity of a metallic conductor is approximately given by, ρT = ρ0 [1 + α (T–T0)] … where ρT is the resistivity at a temperature T and ρ0 is the same at a reference temperature T0. α is called the temperature co-efficient of resistivity …”