*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)  

To understand the frequency response of the circuit in question E7-3 when a capacitor is added across the feedback resistor, we need to analyze how this configuration affects the circuit's behavior.

### Correct Answer: Low-pass filter

1. **Why the correct answer is correct:**
   - Adding a capacitor across the feedback resistor creates a path for high-frequency signals to bypass the resistor. 
   - At low frequencies, the capacitor acts as an open circuit, allowing the feedback resistor to influence the circuit's gain. 
   - As the frequency increases, the capacitor starts to conduct, effectively reducing the feedback at high frequencies. This results in a decrease in gain for high-frequency signals, characteristic of a low-pass filter.

### Why the other choices are incorrect:

2. **High-pass filter (Choice A):**
   - A high-pass filter allows high-frequency signals to pass while attenuating low-frequency signals. This configuration would require a capacitor in series with the input or output, not across the feedback resistor.

3. **Band-pass filter (Choice C):**
   - A band-pass filter allows a specific range of frequencies to pass while attenuating frequencies outside that range. This configuration typically involves both high-pass and low-pass elements, which is not the case here.

4. **Notch filter (Choice D):**
   - A notch filter is designed to attenuate a specific frequency while allowing others to pass. This requires a more complex arrangement, often involving multiple reactive components, rather than just adding a capacitor across a feedback resistor.

### Useful Formulas and Rules of Thumb:

- The cutoff frequency ($f_c$) for a simple RC low-pass filter can be calculated using the formula:
  
  $$f_c = \frac{1}{2 \pi R C}$$

  where:
  - $R$ = resistance in ohms
  - $C$ = capacitance in farads

- The gain of a low-pass filter decreases as frequency increases, typically following a -20 dB/decade slope after the cutoff frequency.

This analysis shows that adding a capacitor across the feedback resistor modifies the circuit to behave as a low-pass filter, allowing low frequencies to pass while attenuating high frequencies.