Question

What is the quality factor ($Q$) of an LCR circuit defined in terms of resonant frequency and bandwidth?

• A. $Q = \frac{\text{Bandwidth}}{f_0}$
• B. $Q = \frac{f_0}{\text{Bandwidth}}$
• C. $Q = f_0 \times \text{Bandwidth}$
• D. $Q = \frac{1}{f_0 \times \text{Bandwidth}}$

Hint:

Remember: High $Q$ = Sharp resonance = Narrow bandwidth.

Answer 1

The Correct Option is B

Concept: The quality factor ($Q$) of a resonant circuit measures the sharpness of resonance.
Step 1: Definition of quality factor.
It is defined as the ratio of resonant frequency to the bandwidth of the circuit.
Step 2: Formula.
\[ Q = \frac{f_0}{\Delta f} \] where $f_0$ is the resonant frequency and $\Delta f$ is the bandwidth.
Step 3: Physical meaning.
Higher $Q$ means sharper resonance and lower energy loss.
Step 4: Evaluating the options.

• $Q = \frac{\text{Bandwidth}}{f_0}$ $\rightarrow$ Incorrect
• $Q = \frac{f_0}{\text{Bandwidth}}$ $\rightarrow$ Correct
• $Q = f_0 \times \text{Bandwidth}$ $\rightarrow$ Incorrect
• $Q = \frac{1}{f_0 \times \text{Bandwidth}}$ $\rightarrow$ Incorrect

Step 5: Conclusion.
Thus, $Q = \frac{f_0}{\text{Bandwidth}}$.