In LCR circuit currnet resonant frequency is 600Hz and half power points are at 650 and 550 Hz. The quality factor is

Options

A. (A) `1/6`
B. (A) `1/3`
C. (C) `6`
D. (D) `3`

Explanation

To find the quality factor (Q) of the LCR circuit, we will follow these steps:

### Step 1: Identify the given values
- Resonant frequency \( f_0 = 600 \, \text{Hz} \)
- Half power points:
- \( f_1 = 550 \, \text{Hz} \)
- \( f_2 = 650 \, \text{Hz} \)

### Step 2: Use the formula for quality factor
The quality factor \( Q \) is given by the formula:
\[ Q = \frac{f_0}{f_2 - f_1} \]

### Step 3: Calculate the difference between the half power points
Calculate \( f_2 - f_1 \):
\[ f_2 - f_1 = 650 \, \text{Hz} - 550 \, \text{Hz} = 100 \, \text{Hz} \]

### Step 4: Substitute the values into the formula
Now substitute \( f_0 \) and \( f_2 - f_1 \) into the formula for \( Q \):
\[ Q = \frac{600 \, \text{Hz}}{100 \, \text{Hz}} \]

### Step 5: Perform the calculation
\[ Q = 6 \]

### Conclusion
The quality factor \( Q \) of the LCR circuit is \( 6 \).

---