The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 10 Ω and at steam point is 10.46 Ω. When the thermometer is inserted in a hot bath, the resistance of the platinum wire is 11.6 Ω. Calculate the temperature of the bath.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 348° C
For a platinum resistance thermometer the resistance varies linearly with temperature, \( R_t = R_0(1 + \alpha t) \), so the temperature is read from its position between the ice point (\( 0^\circ\mathrm{C} \)) and the steam point (\( 100^\circ\mathrm{C} \)):
\( \displaystyle \frac{t - 0}{100 - 0} = \frac{R_t - R_0}{R_{100} - R_0} \)
\( \displaystyle t = \frac{11.6 - 10}{10.46 - 10}\times100^\circ\mathrm{C} = \frac{1.6}{0.46}\times100^\circ\mathrm{C} \approx 348^\circ\mathrm{C} \)
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Temperature Dependence of Resistivity – …
