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**Problem 4 (25 points): Resistors and Capacitors** **Circuit Diagram:** - A schematic is shown with a 5V battery, a capacitor of 100μF, and a 20kΩ resistor connected in series. The circuit includes a switch. **Questions:** 1. **Time Constant, \( t = \) ________________** 2. **Sketch the graph of the voltage when the switch is open after the capacitor has been charged.** - *The capacitor discharges through the resistor, displaying an exponential decay.* 3. **What is the equation of the line?** --- **Explanation:** - **Time Constant (\( \tau \)):** The time constant \(\tau\) is calculated using the formula \(\tau = RC\), where \(R\) is the resistance (20kΩ) and \(C\) is the capacitance (100μF). - **Voltage Graph:** After the switch is open, the voltage across the capacitor decreases exponentially over time. The graph would show the voltage starting at 5V and decaying towards 0V. - **Equation of the Line:** The voltage equation during discharge is described by \( V(t) = V_0 \cdot e^{-t/\tau} \), where \(V_0\) is the initial voltage across the capacitor.

**Problem 4 (25 points): Resistors and Capacitors** **Circuit Diagram:** - A schematic is shown with a 5V battery, a capacitor of 100μF, and a 20kΩ resistor connected in series. The circuit includes a switch. **Questions:** 1. **Time Constant, \( t = \) ________________** 2. **Sketch the graph of the voltage when the switch is open after the capacitor has been charged.** - *The capacitor discharges through the resistor, displaying an exponential decay.* 3. **What is the equation of the line?** --- **Explanation:** - **Time Constant (\( \tau \)):** The time constant \(\tau\) is calculated using the formula \(\tau = RC\), where \(R\) is the resistance (20kΩ) and \(C\) is the capacitance (100μF). - **Voltage Graph:** After the switch is open, the voltage across the capacitor decreases exponentially over time. The graph would show the voltage starting at 5V and decaying towards 0V. - **Equation of the Line:** The voltage equation during discharge is described by \( V(t) = V_0 \cdot e^{-t/\tau} \), where \(V_0\) is the initial voltage across the capacitor.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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I believe the answer for part one of the question is 5 seconds. Need some help solving the other two parts. 

**Problem 4 (25 points): Resistors and Capacitors** **Circuit Diagram:** - A schematic is shown with a 5V battery, a capacitor of 100μF, and a 20kΩ resistor connected in series. The circuit includes a switch. **Questions:** 1. **Time Constant, \( t = \) ________________** 2. **Sketch the graph of the voltage when the switch is open after the capacitor has been charged.** - *The capacitor discharges through the resistor, displaying an exponential decay.* 3. **What is the equation of the line?** --- **Explanation:** - **Time Constant (\( \tau \)):** The time constant \(\tau\) is calculated using the formula \(\tau = RC\), where \(R\) is the resistance (20kΩ) and \(C\) is the capacitance (100μF). - **Voltage Graph:** After the switch is open, the voltage across the capacitor decreases exponentially over time. The graph would show the voltage starting at 5V and decaying towards 0V. - **Equation of the Line:** The voltage equation during discharge is described by \( V(t) = V_0 \cdot e^{-t/\tau} \), where \(V_0\) is the initial voltage across the capacitor.
Transcribed Image Text:**Problem 4 (25 points): Resistors and Capacitors** **Circuit Diagram:** - A schematic is shown with a 5V battery, a capacitor of 100μF, and a 20kΩ resistor connected in series. The circuit includes a switch. **Questions:** 1. **Time Constant, \( t = \) ________________** 2. **Sketch the graph of the voltage when the switch is open after the capacitor has been charged.** - *The capacitor discharges through the resistor, displaying an exponential decay.* 3. **What is the equation of the line?** --- **Explanation:** - **Time Constant (\( \tau \)):** The time constant \(\tau\) is calculated using the formula \(\tau = RC\), where \(R\) is the resistance (20kΩ) and \(C\) is the capacitance (100μF). - **Voltage Graph:** After the switch is open, the voltage across the capacitor decreases exponentially over time. The graph would show the voltage starting at 5V and decaying towards 0V. - **Equation of the Line:** The voltage equation during discharge is described by \( V(t) = V_0 \cdot e^{-t/\tau} \), where \(V_0\) is the initial voltage across the capacitor.
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