At what temperature the resistance of a conductor becomes 20% more than its resistance at 27° C? (The value of the temperature coefficient of resistance of the conductor is 2.0 x 10−4/K.)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1300 K
Resistance increases with temperature as \( R_T = R_{27}(1 + \alpha\,\Delta T) \), with the resistance at 27°C as the reference. A 20% rise means \( R_T = 1.2\,R_{27} \).
\( \displaystyle 1.2 = 1 + \alpha\,\Delta T \)
\( \displaystyle \Delta T = \frac{0.2}{2.0\times10^{-4}\,\mathrm{K^{-1}}} = 1000\,\mathrm{K} \)
\( T_1 = 27^\circ\mathrm{C} = 300\,\mathrm{K} \)
\( \displaystyle T = 300\,\mathrm{K} + 1000\,\mathrm{K} = 1300\,\mathrm{K} \)