On heating a conductor, its resistivity changes by \( 30\% \) of its value at \( 300\ \mathrm{K} \). If the temperature coefficient of resistivity of the conductor is \( 3\times10^{-4}\ /\mathrm{K} \), then its new temperature is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1300\ \mathrm{K} \)
The resistivity of a conductor varies linearly with temperature, with the temperature coefficient of resistivity \( \alpha \) measured from the reference value \( \rho_{0} \):
\( \rho_{T} = \rho_{0}[1 + \alpha(T - T_{0})] \)
So the fractional change in resistivity is:
\( \displaystyle \frac{\rho_{T} - \rho_{0}}{\rho_{0}} = \alpha(T - T_{0}) \)
\( 0.30 = (3\times10^{-4}\,\mathrm{K^{-1}})(T - 300\,\mathrm{K}) \)
\( \displaystyle T - 300\,\mathrm{K} = \frac{0.30}{3\times10^{-4}\,\mathrm{K^{-1}}} = 1000\,\mathrm{K} \)
\( T = 1300\,\mathrm{K} \)