At room temperature (\( 25.0^\circ\mathrm{C} \)) the resistance of a heating element is \( 100\,\Omega \). The temperature of the element at which resistance becomes \( 125.5\,\Omega \) is: (Given that the temperature coefficient of the material of the resistor is \( 1.70 \times 10^{-4}\,^\circ\mathrm{C}^{-1} \).)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1525\,^\circ\mathrm{C} \)
The resistance of a metallic conductor varies linearly with temperature: \( R_{T} = R_{0}\,[\,1 + \alpha\,(T - T_{0})\,] \), where \( \alpha \) is the temperature coefficient of resistance.
\( \displaystyle 125.5 = 100\,[\,1 + 1.70\times10^{-4}\,(T - 25)\,] \)
\( \displaystyle 1.255 - 1 = 1.70\times10^{-4}\,(T - 25) \)
\( \displaystyle T - 25 = \frac{0.255}{1.70\times10^{-4}} = 1500 \)
\( \displaystyle T = 1500 + 25 = 1525\,^\circ\mathrm{C} \)
Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
