*Question E7G02:
What is the frequency response of the circuit in E7-3 if a capacitor is added across the feedback resistor?*  

*Correct Answer is  B: Low-pass filter*  

### AI Response: (may contain errors)  

When a capacitor is added across the feedback resistor in an amplifier circuit, it affects the frequency response of the circuit. Let's break down why this results in a low-pass filter and why the other options are incorrect.

### Explanation:

1. **Correct Answer: Low-pass filter (B)**
   - **Low-pass filter**: This type of filter allows low-frequency signals to pass through while attenuating high-frequency signals. When a capacitor is placed across the feedback resistor, it creates a path for high-frequency signals to bypass the resistor. This effectively reduces the gain for high frequencies, allowing only low frequencies to pass with full gain.
   - **Key Concept**: The impedance of a capacitor decreases with increasing frequency, which means it shunts more of the high-frequency signals away from the output.

2. **Why the other choices are incorrect:**
   - **High-pass filter (A)**: A high-pass filter allows high-frequency signals to pass while attenuating low-frequency signals. This would require a capacitor in series with the input or output, not across the feedback resistor.
   - **Band-pass filter (C)**: A band-pass filter allows a specific range of frequencies to pass while attenuating frequencies outside this range. This typically requires a combination of both high-pass and low-pass elements, not just a single capacitor across a feedback resistor.
   - **Notch filter (D)**: A notch filter attenuates a specific narrow band of frequencies. This requires a more complex arrangement, such as a parallel LC circuit, to create a sharp attenuation at a specific frequency.

### Useful Formula:

The cutoff frequency ($f_c$) for a simple RC low-pass filter can be calculated using the formula:

$$
f_c = \frac{1}{2\pi R_f C}
$$

where:
- $R_f$ is the resistance of the feedback resistor.
- $C$ is the capacitance of the capacitor added across the feedback resistor.

This formula helps determine the frequency at which the filter begins to attenuate the signal.