The value of quality factor is:

Options

A. `(omega L)/(R)`
B. `(omega)/(RC)`
C. `sqrt(LC)`
D. L/R

Answer

To find the value of the quality factor \( Q \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Quality Factor**:
The quality factor \( Q \) is defined as:
\[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]
where \( R \) is the resistance, \( L \) is the inductance, and \( C \) is the capacitance.

2. **Resonance Condition**:
At resonance in an RLC circuit, the inductive reactance \( X_L \) is equal to the capacitive reactance \( X_C \):
\[ X_L = X_C \]
This can be expressed as:
\[ \omega L = \frac{1}{\omega C} \]
where \( \omega \) is the angular frequency.

3. **Rearranging the Resonance Condition**:
From the equation \( \omega L = \frac{1}{\omega C} \), we can multiply both sides by \( \omega \):
\[ \omega^2 = \frac{1}{LC} \]
This implies:
\[ \frac{1}{C} = \omega^2 L \]

4. **Substituting into Quality Factor Formula**:
Now, substitute \( \frac{1}{C} \) back into the quality factor formula:
\[ Q = \frac{1}{R} \sqrt{L \cdot \frac{1}{\omega^2 L}} = \frac{1}{R} \sqrt{\frac{L}{\frac{1}{\omega^2 L}}} \]
Simplifying this gives:
\[ Q = \frac{1}{R} \sqrt{\frac{L^2}{\frac{1}{\omega^2}}} = \frac{1}{R} \cdot \frac{L \omega}{1} \]

5. **Final Expression for Quality Factor**:
Thus, we arrive at the final expression for the quality factor:
\[ Q = \frac{\omega L}{R} \]

### Conclusion:
The value of the quality factor \( Q \) is given by:
\[ Q = \frac{\omega L}{R} \]