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Find and plot the current io(t) and the voltage vo(t) in the circuit shown. t=2 s io(t) 1 mA 20 K2 150 μF 50 µF+ w(t) 20 A2

Find and plot the current io(t) and the voltage vo(t) in the circuit shown. t=2 s io(t) 1 mA 20 K2 150 μF 50 µF+ w(t) 20 A2

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
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**Transcription and Explanation for Educational Purposes:** **Circuit Description:** The circuit diagram shown features a combination of capacitors, resistors, and a current source. Here's a detailed breakdown: 1. **Current Source:** - A constant current source of 1 mA is connected in series with a 20 kΩ resistor. 2. **Resistor:** - The first resistor has a resistance of 20 kΩ. 3. **Capacitors:** - There are two capacitors in parallel: a 150 µF capacitor and a 50 µF capacitor. 4. **Switches and Time Notations:** - The circuit includes a switch, which initially (at \( t = 0 \)) connects the current source and the 20 kΩ resistor with the capacitors. - A second switch position is shown for \( t \geq 2 \) seconds, which redirects the circuit path to add an additional 20 kΩ resistor in parallel with the 50 µF capacitor. 5. **Output Current and Voltage:** - The diagram specifies two quantities to be plotted as functions of time: - \( i_0(t) \): The current through the 50 µF capacitor. - \( v_0(t) \): The voltage across the 50 µF capacitor. **Analysis Objective:** The goal is to determine the behavior of the current \( i_0(t) \) and the voltage \( v_0(t) \) in response to the initial conditions and the change in circuit configuration at \( t = 2 \) seconds. This involves solving the circuit equations for these parameters over time. **Educational Analysis:** To analyze the circuit: - Use Kirchhoff's laws and capacitor charge-discharge equations. - Find the time constants and steady-state responses. - For \( t < 2 \) seconds, consider the initial RC circuit consisting of the 150 µF and 50 µF capacitors in parallel with the resistor. - For \( t \geq 2 \) seconds, analyze the modified circuit configuration when the switch changes position. **Graphical Representation:** The graphs of \( i_0(t) \) and \( v_0(t) \) will typically show exponential charge and discharge curves representing the dynamic response of the capacitors to the changes in the circuit configuration over time.
Transcribed Image Text:**Transcription and Explanation for Educational Purposes:** **Circuit Description:** The circuit diagram shown features a combination of capacitors, resistors, and a current source. Here's a detailed breakdown: 1. **Current Source:** - A constant current source of 1 mA is connected in series with a 20 kΩ resistor. 2. **Resistor:** - The first resistor has a resistance of 20 kΩ. 3. **Capacitors:** - There are two capacitors in parallel: a 150 µF capacitor and a 50 µF capacitor. 4. **Switches and Time Notations:** - The circuit includes a switch, which initially (at \( t = 0 \)) connects the current source and the 20 kΩ resistor with the capacitors. - A second switch position is shown for \( t \geq 2 \) seconds, which redirects the circuit path to add an additional 20 kΩ resistor in parallel with the 50 µF capacitor. 5. **Output Current and Voltage:** - The diagram specifies two quantities to be plotted as functions of time: - \( i_0(t) \): The current through the 50 µF capacitor. - \( v_0(t) \): The voltage across the 50 µF capacitor. **Analysis Objective:** The goal is to determine the behavior of the current \( i_0(t) \) and the voltage \( v_0(t) \) in response to the initial conditions and the change in circuit configuration at \( t = 2 \) seconds. This involves solving the circuit equations for these parameters over time. **Educational Analysis:** To analyze the circuit: - Use Kirchhoff's laws and capacitor charge-discharge equations. - Find the time constants and steady-state responses. - For \( t < 2 \) seconds, consider the initial RC circuit consisting of the 150 µF and 50 µF capacitors in parallel with the resistor. - For \( t \geq 2 \) seconds, analyze the modified circuit configuration when the switch changes position. **Graphical Representation:** The graphs of \( i_0(t) \) and \( v_0(t) \) will typically show exponential charge and discharge curves representing the dynamic response of the capacitors to the changes in the circuit configuration over time.
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