The Q of a resonant transmission line is:

Options

A. `Q=(omega)/(LR)`
B. `Q=(omegaR)/(L)`
C. `Q=(L)/(R)`
D. `Q=(omegaL)/(R)`

Answer

To solve the question regarding the Q of a resonant transmission line, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Quality Factor (Q)**:
The quality factor (Q) is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and it is defined as the ratio of the reactive power to the resistive power in a resonant circuit.

2. **Formula for Quality Factor**:
The formula for the quality factor (Q) in terms of inductive reactance (XL) and resistance (R) is given by:
\[ Q = \frac{X_L}{R} \]
where \(X_L\) is the inductive reactance and \(R\) is the resistance.

3. **Inductive Reactance**:
The inductive reactance (XL) can be expressed in terms of angular frequency (ω) and inductance (L):
\[ X_L = \omega L \]
where:
- \( \omega \) is the angular frequency (in radians per second),
- \( L \) is the inductance (in henries).

4. **Substituting XL in the Q Formula**:
By substituting the expression for \(X_L\) into the Q formula, we get:
\[ Q = \frac{\omega L}{R} \]

5. **Identifying the Correct Option**:
Now, we need to check the given options to find the correct expression for the quality factor of a resonant transmission line. Based on our derived formula, we see that:
\[ Q = \frac{\omega L}{R} \]
matches with option D.

### Conclusion:
Thus, the quality factor (Q) of a resonant transmission line is given by:
\[ Q = \frac{\omega L}{R} \]
and the correct option is **D**.

---