*Question E7C02:
What is the frequency response of a T-network with series capacitors and a shunt inductor?*  

*Correct Answer is  B: High-pass*  

### AI Response: (may contain errors)  

To understand the frequency response of a T-network with series capacitors and a shunt inductor, let's break down the components and their effects on signal frequencies.

### Correct Answer: High-pass

1. **Why the correct answer is correct:**
   - In a T-network with series capacitors, the capacitors allow high-frequency signals to pass while blocking low-frequency signals. The shunt inductor, on the other hand, provides a low impedance path for low frequencies, effectively grounding them.
   - As frequency increases, the reactance of the capacitors decreases, allowing more of the high-frequency signals to pass through. Conversely, the inductor's reactance increases with frequency, which means it will not shunt high frequencies to ground effectively.
   - Therefore, the overall effect of this configuration is to allow high frequencies to pass while attenuating low frequencies, resulting in a high-pass filter response.

### Why the other choices are incorrect:

2. **Low-pass (Choice A):**
   - A low-pass filter allows low frequencies to pass while attenuating high frequencies. This configuration would typically involve series inductors and shunt capacitors, which is the opposite of our T-network.

3. **Band-pass (Choice C):**
   - A band-pass filter allows a specific range of frequencies to pass while attenuating frequencies outside that range. This configuration usually requires both high-pass and low-pass characteristics, which is not the case with our T-network.

4. **Notch (Choice D):**
   - A notch filter is designed to reject a specific frequency while allowing others to pass. This is typically achieved with a combination of series and shunt components that create a resonant circuit, which does not apply to our T-network configuration.

### Useful Formulas and Rules of Thumb:

- **Capacitive Reactance:** The reactance of a capacitor is given by:
  $$X_C = \frac{1}{2 \pi f C}$$
  where:
  - $X_C$ = capacitive reactance (ohms)
  - $f$ = frequency (hertz)
  - $C$ = capacitance (farads)

- **Inductive Reactance:** The reactance of an inductor is given by:
  $$X_L = 2 \pi f L$$
  where:
  - $X_L$ = inductive reactance (ohms)
  - $L$ = inductance (henries)

### Summary:
- The T-network with series capacitors and a shunt inductor acts as a high-pass filter because it allows high-frequency signals to pass while blocking low-frequency signals. Understanding the behavior of capacitors and inductors at different frequencies is key to identifying the filter type.