Question:
A heating element has a resistance of \(100\ \Omega\) at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is \(500^\circ\mathrm{C}\) more than room temperature. What is the temperature coefficient of resistance of the heating element ?
A heating element has a resistance of \(100\ \Omega\) at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is \(500^\circ\mathrm{C}\) more than room temperature. What is the temperature coefficient of resistance of the heating element ?
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Find the hot resistance \(R = V/I\) and use \(R = R_0(1 + \alpha \Delta T)\).
Updated On: Nov 11, 2026
- \(0.5 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\)
- \(5 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\)
- \(1 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\)
- \(2 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\)
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The Correct Option is D
Solution and Explanation
Resistance at the working temperature: \(R = \frac{V}{I} = \frac{220}{2} = 110\ \Omega\).
With \(R_0 = 100\ \Omega\) and \(\Delta T = 500^\circ\mathrm{C}\): \(R = R_0(1 + \alpha\Delta T)\).
\(110 = 100(1 + 500\alpha)\) so \(500\alpha = 0.1\).
\(\alpha = 2 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\).
Answer: (4) \(2 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\)
With \(R_0 = 100\ \Omega\) and \(\Delta T = 500^\circ\mathrm{C}\): \(R = R_0(1 + \alpha\Delta T)\).
\(110 = 100(1 + 500\alpha)\) so \(500\alpha = 0.1\).
\(\alpha = 2 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\).
Answer: (4) \(2 \times 10^{-4}\ {}^\circ\mathrm{C}^{-1}\)
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