The resistance of a wire at room temperature (\( 25\,^\circ\mathrm{C} \)) is \( 100\,\Omega \). Now a current of \( 2\,\mathrm{A} \) at \( 220\,\mathrm{V} \) flows in the wire for some time till the temperature of the wire becomes \( 900\,^\circ\mathrm{C} \). The temperature coefficient of resistance of wire is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 1.14\times10^{-4}\,^\circ\mathrm{C}^{-1} \)
Over a temperature range the resistance changes as \( R_T = R_0[1 + \alpha(T - T_0)] \), where \( \alpha \) is the temperature coefficient of resistance.
The hot resistance comes from Ohm’s law using the given current and voltage:
\( R_{900} = V/I = 220/2 = 110\,\Omega \)
\( R_0 = 100\,\Omega \text{ at } 25\,^\circ\mathrm{C} \)
\( \Delta T = 900 - 25 = 875\,^\circ\mathrm{C} \)
\( \displaystyle \alpha = \frac{R_T - R_0}{R_0\,\Delta T} = \frac{110 - 100}{100\times875}\,^\circ\mathrm{C}^{-1} \)
\( \displaystyle \alpha = \frac{10}{87500} \approx 1.14\times10^{-4}\,^\circ\mathrm{C}^{-1} \)