*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 transforms the impedance in a specific way due to the properties of transmission lines.

### Explanation:

1. **Correct Answer: Very high impedance (A)**

   - A 1/4-wavelength transmission line acts as an impedance transformer. When the line is shorted at the far end, the impedance at the input (near the RF generator) becomes very high. This is because a short circuit at the end of a 1/4-wavelength line transforms to an open circuit at the input.
   - The transformation property of a 1/4-wavelength line is given by:
     $$ Z_{\text{in}} = \frac{Z_0^2}{Z_{\text{load}}} $$
     where:
     - $Z_{\text{in}}$ is the input impedance.
     - $Z_0$ is the characteristic impedance of the line.
     - $Z_{\text{load}}$ is the load impedance (0 for a short circuit).
   - Since $Z_{\text{load}} = 0$ (short circuit), $Z_{\text{in}}$ becomes very large (approaching infinity).

2. **Why the other choices are incorrect:**

   - **B: Very low impedance**
     - This would be true if the line were 1/2-wavelength long, as a short at the end of a 1/2-wavelength line appears as a short at the input. However, for a 1/4-wavelength line, the impedance is transformed to a high value.

   - **C: The same as the characteristic impedance of the transmission line**
     - This would occur if the line were terminated with a load equal to its characteristic impedance, not when shorted.

   - **D: The same as the generator output impedance**
     - The generator output impedance is not directly related to the transformation properties of the transmission line. The line's transformation depends on its length and termination, not the generator's impedance.

### Key Rule of Thumb:

- A 1/4-wavelength transmission line transforms a short circuit to an open circuit (very high impedance) and vice versa. This is a fundamental property of transmission lines used in impedance matching and RF design.