A wire has a resistance of \( 3\,\Omega \) at 20 °C and \( 5\,\Omega \) at 100 °C. The temperature coefficient of resistance of the wire is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 0.00833\,^\circ\mathrm{C}^{-1} \)
The temperature coefficient of resistance is the fractional change in resistance per degree, measured from the resistance at the reference temperature (here 20 °C).
\( \displaystyle R_2 = R_1\left[1 + \alpha\,(T_2 - T_1)\right] \)
\( \displaystyle \alpha = \frac{R_2 - R_1}{R_1\,(T_2 - T_1)} = \frac{(5 - 3)\,\Omega}{3\,\Omega \times (100 - 20)\,^\circ\mathrm{C}} = \frac{2}{240}\,^\circ\mathrm{C}^{-1} = 0.00833\,^\circ\mathrm{C}^{-1} \)
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 – …
