Question

Resonance frequency of LCR series a.c. circuit is \( f_0 \). Now the capacitance is made 4 times, then the new resonance frequency will become

• A. \( \frac{f_0}{4} \)
• B. \( \frac{f_0}{2} \)
• C. \( 2f_0 \)
• D. \( f_0 / 2 \)

Hint:

In an LCR circuit, the resonance frequency is inversely proportional to the square root of the capacitance.

Answer 1

The Correct Option is B

Step 1: Use the formula for resonance frequency.
The resonance frequency for an LCR circuit is given by: \[ f_0 = \frac{1}{2 \pi \sqrt{LC}} \]
Step 2: Modify the formula with the change in capacitance.
If the capacitance \( C \) is made 4 times larger, the new resonance frequency becomes: \[ f_{\text{new}} = \frac{f_0}{2} \]
Final Answer: \[ \boxed{\frac{f_0}{2}} \]