Question

From the figure shown below, a series LCR circuit connected to a variable frequency 200V source. \( L = 5H, C = 80 \mu F, R = 40 \Omega \). Then the source frequency which drives the circuit at resonance is

• A. 25 Hz
• B. \( \frac{25}{\pi} \) Hz
• C. 50 Hz
• D. \( \frac{50}{\pi} \) Hz

Hint:

At resonance, the inductive and capacitive reactances are equal, and the impedance is purely resistive.

Answer 1

The Correct Option is B

Step 1: Resonance condition.
At resonance in an LCR circuit, the inductive reactance and capacitive reactance cancel out. The resonance frequency \( f_0 \) is given by: \[ f_0 = \frac{1}{2\pi \sqrt{LC}} \] Substituting the values of \( L \) and \( C \), we get the resonance frequency.

Step 2: Conclusion.
Thus, the resonance frequency is \( \frac{25}{\pi} \) Hz. Hence, the correct answer is option (B).

Final Answer: \[ \boxed{\frac{25}{\pi} \, \text{Hz}} \]