The resistance of a conductor at 27° C is 100 Ω. The temperature at which the resistance of the conductor becomes 117 Ω is:
(Given the temperature coefficient of resistance α = 1.70 × 10−4 °C−1)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1027 °C
Over a moderate temperature range the resistance of a conductor increases linearly with temperature, with slope set by the temperature coefficient of resistance \( \alpha \). Take the resistance at 27 °C as the reference value.
\( \displaystyle R_T = R_{27}\left[1 + \alpha\,(T - 27\,^\circ\mathrm{C})\right] \)
\( \displaystyle 117\,\Omega = 100\,\Omega\left[1 + 1.70\times10^{-4}\,^\circ\mathrm{C}^{-1} \times (T - 27\,^\circ\mathrm{C})\right] \)
\( \displaystyle T - 27\,^\circ\mathrm{C} = \frac{0.17}{1.70\times10^{-4}\,^\circ\mathrm{C}^{-1}} = 1000\,^\circ\mathrm{C} \)
\( T = 1027\,^\circ\mathrm{C} \)
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
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