Question

In an LCR resonance circuit at resonance frequency \( \omega_0 \), the quality factor \( Q \) is:

• A. \( \omega_0 L R \)
• B. \( \omega_0 L C \)
• C. \( \frac{\omega_0}{L R} \)
• D. \( \omega_0 \sqrt{L C} \)
• E. \( \frac{\omega_0 L}{R} \)

Hint:

The quality factor \( Q \) of a resonant LCR circuit is related to the resonance frequency, the inductance, and the resistance of the circuit. A higher \( Q \) means a sharper resonance and less energy loss.

Answer 1

Answer: (E)

The quality factor \( Q \) of a resonance circuit is a measure of the sharpness of the resonance. It is defined as the ratio of the resonant frequency to the bandwidth. For an LCR circuit, at resonance frequency \( \omega_0 \), the quality factor \( Q \) is given by: \[ Q = \frac{\omega_0 L}{R} \] where: - \( \omega_0 \) is the resonance frequency,
- \( L \) is the inductance,
- \( R \) is the resistance.
This expression indicates that the quality factor \( Q \) is directly proportional to the inductance \( L \) and the resonance frequency \( \omega_0 \), and inversely proportional to the resistance \( R \).
Thus, the correct answer is: \[ \boxed{\frac{\omega_0 L}{R}} \]