Question

The resonant frequency of a series RLC circuit is

• A. \(\frac{1}{2\pi LC}\)
• B. \(\frac{1}{2\pi\sqrt{LC}}\)
• C. \(2\pi\sqrt{LC}\)
• D. \(\frac{L}{C}\)

Hint:

Resonant frequency of an RLC circuit is \(f_0=\frac{1}{2\pi\sqrt{LC}}\).

Answer 1

The Correct Option is B

Concept: At resonance in an RLC circuit: \[ X_L=X_C \]

Step 1: Write reactances: \[ X_L=2\pi fL \] and: \[ X_C=\frac{1}{2\pi fC} \]

Step 2: At resonance: \[ 2\pi fL=\frac{1}{2\pi fC} \]

Step 3: Rearranging: \[ (2\pi f)^2LC=1 \] \[ f^2=\frac{1}{4\pi^2LC} \] \[ f=\frac{1}{2\pi\sqrt{LC}} \] Therefore: \[ \boxed{\frac{1}{2\pi\sqrt{LC}}} \]