*Question E9F10:
What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is shorted at the far end?*  

*Correct Answer is  C: An inductive reactance*  

### AI Response: (may contain errors)  

To understand the impedance presented by a 1/8-wavelength transmission line that is shorted at the far end, we need to consider how transmission lines behave.

### Correct Answer: An inductive reactance

1. **Why the correct answer is correct:**
   - A transmission line that is shorted at the far end reflects the short circuit back towards the generator. The length of the line (1/8 wavelength) causes the impedance to transform.
   - For a shorted line, the impedance at the generator end can be calculated using the formula for a transmission line:
     $$ Z_{in} = j Z_0 \tan(\beta l) $$
   - Here, $Z_0$ is the characteristic impedance, $\beta$ is the phase constant, and $l$ is the length of the line. For a 1/8 wavelength line, $\beta l = \frac{\pi}{4}$.
   - Thus, the impedance becomes:
     $$ Z_{in} = j Z_0 \tan\left(\frac{\pi}{4}\right) = j Z_0 $$
   - This indicates that the impedance is purely inductive, as it has a positive imaginary component.

### Why the other choices are incorrect:

2. **Choice A: A capacitive reactance**
   - A capacitive reactance would imply that the impedance has a negative imaginary component. However, a shorted line transforms to an inductive reactance, not capacitive.

3. **Choice B: The same as the characteristic impedance of the line**
   - This would only be true if the line were open-circuited at the far end. Since the line is shorted, the impedance is transformed and does not equal the characteristic impedance.

4. **Choice C: An inductive reactance**
   - This choice is actually correct, but it is not the answer provided in the question. The correct answer is that the impedance is an inductive reactance, which is what we have established.

5. **Choice D: Zero**
   - A zero impedance would imply a perfect short circuit, which does not account for the transformation effects of the transmission line. The impedance is not zero; it is an inductive reactance.

### Summary:
- The impedance of a 1/8-wavelength transmission line shorted at the far end presents an inductive reactance due to the transformation of the short circuit back towards the generator. The correct answer is that it presents an inductive reactance, which is a key concept in understanding transmission line behavior.