*Question E9F09:
What impedance does a 1/4-wavelength transmission line present to an RF generator when the line is shorted at the far end?*  

*Correct Answer is  A: Very high impedance*  

### AI Response: (may contain errors)  

When a 1/4-wavelength transmission line is shorted at the far end, it presents a very high impedance to the RF generator. Here's why:

1. **Correct Answer Explanation (Very High Impedance)**:
   - A 1/4-wavelength transmission line transforms the impedance at its input based on the load at its output. When the line is shorted (0 ohms) at the far end, the input impedance ($Z_{in}$) can be calculated using the formula:
   $$
   Z_{in} = \frac{Z_0^2}{Z_L}
   $$
   where:
   - $Z_0$ = characteristic impedance of the transmission line
   - $Z_L$ = load impedance (0 ohms for a short)
   
   Substituting $Z_L = 0$ gives:
   $$
   Z_{in} = \frac{Z_0^2}{0} \rightarrow \text{very high impedance}
   $$
   This means that the RF generator sees a very high impedance, effectively blocking the current flow.

2. **Incorrect Answer Explanations**:
   - **A: Very low impedance**: This is incorrect because a shorted line presents a high impedance to the generator, not low. A short circuit would present a low impedance.
   - **C: The same as the characteristic impedance of the transmission line**: This is incorrect because the input impedance is not equal to the characteristic impedance when the line is shorted. Instead, it becomes very high.
   - **D: The same as the generator output impedance**: This is incorrect because the generator output impedance does not change based on the load at the end of the transmission line. The input impedance seen by the generator is transformed by the transmission line.

3. **Useful Formulas and Rules of Thumb**:
   - For a 1/4-wavelength line:
     - Shorted load ($Z_L = 0$) results in very high input impedance.
     - Open load ($Z_L = \infty$) results in very low input impedance.
   - Remember that the transformation of impedance is a key concept in transmission line theory, especially for quarter-wave lines. 

This understanding is crucial for effectively using transmission lines in RF applications and for passing the Extra Class exam.