*Question E9A10:
Which of the following improves the efficiency of a ground-mounted quarter-wave vertical antenna?*  

*Correct Answer is  A: Installing a ground radial system*  

### AI Response: (may contain errors)  

To improve the efficiency of a ground-mounted quarter-wave vertical antenna, the correct answer is:

**A: Installing a ground radial system**

### Explanation of the Correct Answer:
- **Ground Radial System**: A ground radial system consists of several wires or radials that are laid out horizontally on the ground. This system provides a better ground reference for the antenna, which helps to improve its radiation efficiency. The radials act as a mirror for the radiated energy, effectively increasing the antenna's performance by reducing losses.

### Why the Other Choices are Incorrect:
- **B: Isolating the coax shield from ground**: 
  - Isolating the coax shield can actually lead to increased losses and poor performance. The coax shield is typically grounded to provide a return path for the RF current and to minimize interference. If the shield is isolated, it may not effectively serve its purpose, leading to inefficiencies.

- **C: Shortening the radiating element**: 
  - Shortening the radiating element of a quarter-wave vertical antenna will decrease its efficiency. A quarter-wave antenna is designed to be approximately $L = \frac{c}{4f}$, where $c$ is the speed of light and $f$ is the frequency. Shortening it will result in a mismatch and reduced radiation efficiency.

- **D: All these choices are correct**: 
  - Since only choice A is correct, this option is incorrect as well.

### Useful Formulas:
- The length of a quarter-wave vertical antenna can be calculated using the formula:
$$
L = \frac{c}{4f}
$$
where:
- $L$ = length of the antenna in meters
- $c$ = speed of light (approximately $3 \times 10^8$ m/s)
- $f$ = frequency in hertz

### Summary:
To enhance the efficiency of a ground-mounted quarter-wave vertical antenna, installing a ground radial system is essential. The other options either do not contribute positively to efficiency or detract from it.