Question

An electric lamp connected in series with a capacitor and an a.c. source is glowing with certain brightness. On reducing the capacitance and frequency, the brightness of the lamp respectively

• A. is increased, is increased
• B. is reduced, is increased
• C. is increased, is reduced
• D. is reduced, is reduced

Hint:

Brightness of an AC lamp depends on current, which is controlled by reactance.

Answer 1

The Correct Option is D

Step 1: Capacitive reactance.
\[ X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C} \]
Step 2: Effect of reducing capacitance.
If \(C\) decreases, \(X_C\) increases, current decreases, so brightness decreases.
Step 3: Effect of reducing frequency.
If \(f\) decreases, \(X_C\) increases, current decreases further.
Step 4: Conclusion.
In both cases, lamp current reduces, hence brightness reduces.