Question

What is the physical significance of the "Quality Factor" (\(Q\)-factor) in an LCR resonant circuit?

• A. It represents the resistance of the circuit
• B. It measures the sharpness of resonance
• C. It determines the supply voltage
• D. It gives the current amplitude directly

Hint:

Higher \(Q\)-factor → sharper resonance and smaller bandwidth. Lower \(Q\)-factor → broader resonance.

Answer 1

The Correct Option is B

Concept: The Quality Factor (Q-factor) of an LCR circuit indicates how sharply the circuit resonates at its resonant frequency. Mathematically, \[ Q = \frac{\omega_0 L}{R} \] or equivalently \[ Q = \frac{1}{R}\sqrt{\frac{L}{C}} \] where

• \(L\) = inductance
• \(C\) = capacitance
• \(R\) = resistance
• \(\omega_0\) = resonant angular frequency

Step 1: Interpretation of Q-factor.} A high \(Q\)-factor means the circuit has:

• Low energy loss
• Narrow bandwidth
• Sharp resonance peak

Step 2: Bandwidth relation.} \[ Q = \frac{\omega_0}{\Delta \omega} \] where \(\Delta \omega\) is the bandwidth.
Step 3: Conclusion.} Therefore, the Q-factor describes the sharpness or selectivity of resonance in the circuit.