MHT CET · Physics · Alternating Current
The \(Q\) -factor of a resonant circuit is equal to
- A \(\frac{1}{L} \sqrt{\frac{R}{C}}\)
- B \(\frac{1}{R} \sqrt{\frac{L}{C}}\)
- C \(\frac{1}{R L} \sqrt{C}\)
- D \(\frac{1}{C} \sqrt{\frac{R}{L}}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{R} \sqrt{\frac{L}{C}}\)
Step-by-step Solution
Detailed explanation
The quality factor (Q-factor) of a resonant circuit
\(
Q=\frac{\omega_{0} L}{R}
\)
At resonance, \(\omega_{0}=\frac{1}{\sqrt{L C}}\)
\(
Q=\frac{1}{\sqrt{L} C} \cdot \frac{L}{R}=\frac{1}{R} \sqrt{\frac{L}{C}}
\)
\(
Q=\frac{\omega_{0} L}{R}
\)
At resonance, \(\omega_{0}=\frac{1}{\sqrt{L C}}\)
\(
Q=\frac{1}{\sqrt{L} C} \cdot \frac{L}{R}=\frac{1}{R} \sqrt{\frac{L}{C}}
\)
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