Question

An electric bulb of 100 W is connected to a supply of electricity of 220 V. The resistance of the filament is:

• A. 484 \( \Omega \)
• B. 100 \( \Omega \)
• C. 22000 \( \Omega \)
• D. 242 \( \Omega \)

Hint:

Power dissipated in a resistor is directly proportional to the square of the voltage and inversely proportional to the resistance.

Answer 1

The Correct Option is B

Step 1: Use the power formula.
The power dissipated in a resistor is given by: \[ P = \frac{V^2}{R} \] where \( P \) is the power, \( V \) is the voltage, and \( R \) is the resistance.
Step 2: Solve for resistance.
Rearranging the formula, we find: \[ R = \frac{V^2}{P} = \frac{220^2}{100} = 484 \, \Omega \]
Final Answer: \[ \boxed{484 \, \Omega} \]