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 factor of a resonant transmission line, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Q Factor**:
The Q factor, or quality factor, is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and it characterizes the resonant frequency and bandwidth of the system.

2. **Formula for Q Factor**:
The Q factor can be defined as:
\[ Q = \frac{F_R}{BW} \]
where \( F_R \) is the resonant frequency and \( BW \) is the bandwidth of the resonant system.

3. **Relate Q Factor to Series LCR Circuit**:
For a series LCR circuit, the Q factor can also be expressed in terms of its components:
\[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]
This shows that the Q factor is dependent on the resistance (R), inductance (L), and capacitance (C) of the circuit.

4. **Simplifying the Expression**:
From the above formula, we can rearrange it to express Q in terms of L and R:
\[ Q = \frac{L}{R} \]
This indicates that the quality factor is directly proportional to the inductance and inversely proportional to the resistance.

5. **Conclusion**:
Based on the derived formulas and understanding of the Q factor, we can conclude that for a resonant transmission line modeled as a series LCR circuit, the Q factor is given by:
\[ Q = \frac{L}{R} \]

### Final Answer:
The Q of a resonant transmission line is \( \frac{L}{R} \).

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