1. Given data

• Resistance at room temperature: $R_0 = 100\,\Omega$
• Supply voltage: $V = 220\,\text{V}$
• Steady current at higher temperature: $I = 2\,\text{A}$
• Rise in temperature: $\Delta T = 500^\circ \text{C}$

2. Find the resistance at the higher temperature

Using Ohm’s law, $R = \frac{V}{I} = \frac{220}{2} = 110\,\Omega$

So, at the elevated temperature, the resistance becomes $R = 110\,\Omega$

3. Use the linear relation for resistance with temperature

For small/moderate temperature ranges, resistance varies as $R = R_0(1 + \alpha \Delta T)$

Substitute the values: $110 = 100(1 + \alpha \times 500)$

4. Solve for $\alpha$

Divide both sides by 100: $1.1 = 1 + 500\alpha$

$500\alpha = 0.1$

$\alpha = \frac{0.1}{500} = 2 \times 10^{-4}\,^\circ\text{C}^{-1}$

5. Match with the options

$\alpha = 2 \times 10^{-4}\,^\circ\text{C}^{-1}$

This corresponds to Option D.

6. Verification with stored answer

Stored correct answer: D

Our derived answer: D

So, the answer agrees with the stored correct answer.