Numbers 15 and 16 (it's not incomplete).

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Numbers 15 and 16 (it's not incomplete).

**Section 13–3: Integrators and Differentiators**

**Problem 15:**
Determine the rate of change of the output voltage in response to the step input to the integrator in Figure 13–68.

*Diagram Description:*
- The circuit in Figure 13–68 includes a 56 kΩ resistor and a 0.022 μF capacitor connected to an operational amplifier (op-amp). 
- The input voltage \( V_{\text{in}} \) is a step function with a voltage of 5 V.

**Problem 16:**
A triangular waveform is applied to the input of the circuit in Figure 13–69 as shown. Determine what the output should be and sketch its waveform in relation to the input.

*Diagram Description:*
- The input is a triangular waveform with a peak voltage of 5 V and a period of 10 μs.
- The circuit contains a 10 kΩ resistor and a 0.001 μF capacitor connected to an op-amp.

**Problem 17:**
What is the magnitude of the capacitor current in Problem 16?

**Problem 18:**
A triangular waveform with a peak-to-peak voltage of 2 V and a period of 1 ms is applied to the differentiator in Figure 13–70(a). What is the output voltage?

**Problem 19:**
Beginning in position 1 in Figure 13–70(b), the switch is thrown into position 2 and held there for 10 ms, then back to position 1 for 10 ms, and so forth. Sketch the resulting output waveform if its initial value is 0 V. The saturated output levels of the op-amp are ± 12 V.

*Diagram Descriptions:*
- **Figure 13–70(a):**
  - Circuit includes a 15 kΩ resistor and a 0.047 μF capacitor connected to an op-amp.

- **Figure 13–70(b):**
  - Circuit features a +5 V and -5 V power supply, a 10 kΩ resistor, and a 10 μF capacitor connected to an op-amp.
Transcribed Image Text:**Section 13–3: Integrators and Differentiators** **Problem 15:** Determine the rate of change of the output voltage in response to the step input to the integrator in Figure 13–68. *Diagram Description:* - The circuit in Figure 13–68 includes a 56 kΩ resistor and a 0.022 μF capacitor connected to an operational amplifier (op-amp). - The input voltage \( V_{\text{in}} \) is a step function with a voltage of 5 V. **Problem 16:** A triangular waveform is applied to the input of the circuit in Figure 13–69 as shown. Determine what the output should be and sketch its waveform in relation to the input. *Diagram Description:* - The input is a triangular waveform with a peak voltage of 5 V and a period of 10 μs. - The circuit contains a 10 kΩ resistor and a 0.001 μF capacitor connected to an op-amp. **Problem 17:** What is the magnitude of the capacitor current in Problem 16? **Problem 18:** A triangular waveform with a peak-to-peak voltage of 2 V and a period of 1 ms is applied to the differentiator in Figure 13–70(a). What is the output voltage? **Problem 19:** Beginning in position 1 in Figure 13–70(b), the switch is thrown into position 2 and held there for 10 ms, then back to position 1 for 10 ms, and so forth. Sketch the resulting output waveform if its initial value is 0 V. The saturated output levels of the op-amp are ± 12 V. *Diagram Descriptions:* - **Figure 13–70(a):** - Circuit includes a 15 kΩ resistor and a 0.047 μF capacitor connected to an op-amp. - **Figure 13–70(b):** - Circuit features a +5 V and -5 V power supply, a 10 kΩ resistor, and a 10 μF capacitor connected to an op-amp.
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