NCERT · Class 12 · Physics · Alternating CurrentThe resonant frequency ($fr$) of a series LCR circuit is given by:
Step-by-Step Solution
At resonance, $X_L = X_C \implies 2\pi f L = \frac{1}{2\pi f C}$. Solving for frequency gives $f_r = \frac{1}{2\pi \sqrt{LC}}$.
Detailed Options Breakdown
Option : $\frac{1}{2\pi \sqrt{LC}}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $2\pi \sqrt{LC}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Alternating Current.
Option 2: $\frac{1}{2\pi} \sqrt{\frac{L}{C}}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Alternating Current.
Option 3: $\frac{1}{2\pi} \sqrt{\frac{C}{L}}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Alternating Current.
💡 Study Guide: This question tests core syllabus concepts from Alternating Current. For formulas, key summaries, and mock exam reference guides, read the full Alternating Current Revision Notes.