*Question E5A11:
What is the half-power bandwidth of a resonant circuit that has a resonant frequency of 7.1 MHz and a Q of 150?*  

*Correct Answer is  C: 47.3 kHz*  

### AI Response: (may contain errors)  

To determine the half-power bandwidth of a resonant circuit, we use the formula:

$$
BW = \frac{f_0}{Q}
$$

where:
- $BW$ is the bandwidth in hertz (Hz),
- $f_0$ is the resonant frequency in hertz (Hz),
- $Q$ is the quality factor (unitless).

Given:
- $f_0 = 7.1 \, \text{MHz} = 7,100,000 \, \text{Hz}$
- $Q = 150$

Substitute these values into the formula:

$$
BW = \frac{7,100,000}{150} = 47,333.33 \, \text{Hz}
$$

This result is approximately 47.3 kHz, which matches choice C.

### Explanation of Choices:

- **A: 157.8 Hz**  
  This value is too low. It would imply a much higher $Q$ factor or a much lower resonant frequency.

- **B: 315.6 Hz**  
  This value is also too low. It suggests a $Q$ factor or resonant frequency that does not match the given values.

- **C: 47.3 kHz**  
  This is the correct answer. It accurately reflects the calculated bandwidth using the given resonant frequency and $Q$ factor.

- **D: 23.67 kHz**  
  This value is too low. It would imply a $Q$ factor of approximately 300, which is not the case here.

### Key Points:
- The half-power bandwidth is inversely proportional to the $Q$ factor.
- A higher $Q$ results in a narrower bandwidth, while a lower $Q$ results in a wider bandwidth.
- Always ensure units are consistent when performing calculations.