Question

The plot given below is of the average power delivered to an LRC circuit versus frequency. The quality factor of the circuit is:

• A. 5
• B. 2
• C. 2.5
• D. 4,0

Answer 1

The correct option is B

2

Step 1: Given data and the diagram

From the graph,

Resonating frequency (at which the peak occurs) ${\omega }_0=5\text{khz}$

Bandwidth, $2∆\mathrm{\omega }={\mathrm{\omega }}_2-{\mathrm{\omega }}_1=2.5\text{khz}$ (Frequency when the power is half of the peak)

Step 2: To Find

The quality factor of the circuit

Step 3: Calculate the quality factor

We know the formula,

$$\begin{gathered} Q=\frac{{\mathrm{\omega }}_0}{2∆\mathrm{\omega }} \\ =\frac{5\text{khz}}{2.5\text{khz}} \\ =2 \end{gathered}$$

Hence, option (B) is correct.