Question

In LCR circuit, at a particular angular frequency the capacitive reactance and inductive reactance is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

• A. \(\frac{1}{4}\)
• B. \(\frac{1}{2}\)
• C. \(1\)
• D. \(4\)

Hint:

Capacitive reactance rises as frequency falls, so the current decreases.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In an AC circuit with a lamp (resistance R) and a capacitor, the impedance is \(Z = \sqrt{R^2 + X_C^2}\) with \(X_C = \frac{1}{2\pi fC}\).

Step 2: Effect of lowering f:
When f decreases, \(X_C\) increases, so Z increases and the current \(I = \frac VZ\) decreases. The lamp's power \(I^2R\) falls, so the lamp becomes dimmer. It does not become completely dark, because the current is still non-zero at any finite frequency.

Final Answer:
The brightness of the lamp is reduced, option (B). \[ \boxed{\text{is reduced}} \]