*Question E7C01:
How are the capacitors and inductors of a low-pass filter Pi-network arranged between the network’s input and output?*  

*Correct Answer is  D: A capacitor is connected between the input and ground, another capacitor is connected between the output and ground, and an inductor is connected between the input and output*  

### AI Response: (may contain errors)  

In a low-pass filter Pi-network, the arrangement of components is crucial for its function. The correct answer is:

**Correct Answer: D**  
A capacitor is connected between the input and ground, another capacitor is connected between the output and ground, and an inductor is connected between the input and output.

### Explanation of the Correct Answer:
- In a Pi-network low-pass filter, the configuration consists of:
  - **Two capacitors**: One connected from the input to ground and the other from the output to ground. These capacitors allow low-frequency signals to pass while blocking high-frequency signals.
  - **One inductor**: This is connected between the input and output. The inductor provides a path for low-frequency signals while presenting a high impedance to high-frequency signals, effectively filtering them out.

### Why the Other Choices are Incorrect:
- **Choice A**: Two inductors in series with a capacitor between them and ground.
  - This configuration does not represent a Pi-network. It would create a band-pass or notch filter rather than a low-pass filter.

- **Choice B**: Two capacitors in series with an inductor between them and ground.
  - This arrangement does not provide the necessary low-pass characteristics. It would also not effectively ground the input and output as required for a Pi-network.

- **Choice C**: An inductor connected between the input and ground, another inductor connected between the output and ground, and a capacitor between the input and output.
  - This configuration resembles a high-pass filter rather than a low-pass filter. It does not allow low frequencies to pass effectively.

### Useful Formulas and Rules of Thumb:
- The cutoff frequency ($f_c$) for a low-pass filter can be calculated using the formula:
  
  $$f_c = \frac{1}{2\pi\sqrt{LC}}$$

  where:
  - $L$ = inductance in henries
  - $C$ = capacitance in farads

- A rule of thumb for designing low-pass filters is to ensure that the inductor's reactance at the cutoff frequency is equal to the resistance of the load, which helps in achieving the desired filtering effect.

Understanding these configurations and their implications will help you in both the exam and practical applications in amateur radio.