A wire has a resistance of \( 3.0\,\Omega \) at \( 30^\circ\mathrm{C} \) and a resistance of \( 4.5\,\Omega \) at \( 100^\circ\mathrm{C} \). The temperature coefficient of resistance of the wire is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 0.0071\,^\circ\mathrm{C^{-1}} \)
The temperature coefficient of resistance \( \alpha \) is the fractional change in resistance per degree, measured from the lower temperature: \( R_2 = R_1\,[1 + \alpha\,(T_2 - T_1)] \).
\( \displaystyle \alpha = \frac{R_2 - R_1}{R_1\,(T_2 - T_1)} = \frac{4.5 - 3.0}{3.0 \times (100 - 30)} = \frac{1.5}{210} \)
\( \displaystyle \alpha = 7.1\times10^{-3}\ ^\circ\mathrm{C^{-1}} = 0.0071\ ^\circ\mathrm{C^{-1}} \)
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 – …
