1. Given data

   • Bulb rating: $500\,\text{W}$ at $100\,\text{V}$
   • Supply voltage: $200\,\text{V}$
   • We need a series resistance $R$ so that the bulb still gets power $500\,\text{W}$.

2. Find the current through the bulb at its rated condition Since the bulb must operate at $500\,\text{W}$ and $100\,\text{V}$, $P = VI$ $500 = 100 \cdot I$ $I = 5\,\text{A}$

3. Voltage across the series resistor The supply is $200\,\text{V}$, while the bulb should have only $100\,\text{V}$ across it. So the remaining voltage must drop across the series resistor: $V_R = 200 - 100 = 100\,\text{V}$

4. Find the required resistance The same current $5\,\text{A}$ flows through the bulb and the series resistor. Using Ohm’s law: $R = \frac{V_R}{I} = \frac{100}{5} = 20\,\Omega$

5. Check options

   • A: $20\,\Omega$ ✅
   • B: $30\,\Omega$ ❌
   • C: $5\,\Omega$ ❌
   • D: $10\,\Omega$ ❌

Therefore, the correct answer is A: $20\,\Omega$.