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(b) After being opened for a long time, the switch in the circuit closes at t = 0. Compute ve(t) for t 0, where: vc (t) = vc (0) + [vc (0+) - vc(oo)]e-( 5V + 252 352 t=0 0.3μF/ Ve +

(b) After being opened for a long time, the switch in the circuit closes at t = 0. Compute ve(t) for t 0, where: vc (t) = vc (0) + [vc (0+) - vc(oo)]e-( 5V + 252 352 t=0 0.3μF/ Ve +

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Transcription for Educational Use (b) After being opened for a long time, the switch in the circuit closes at \( t = 0 \). Compute \( v_c(t) \) for \( t \geq 0 \), where: \[ v_c(t) = v_c(\infty) + [v_c(0^+) - v_c(\infty)]e^{-\frac{t}{\tau}} \] #### Circuit Diagram Explanation - **Voltage Source:** There is a 5V voltage source in the circuit. - **Resistors:** Two resistors are present: - One with a resistance of 2Ω (ohms). - Another with a resistance of 3Ω (ohms). - **Capacitor:** A capacitor with a capacitance of 0.3μF (microfarads) is in the circuit. - **Switch:** The switch in the circuit closes at \( t = 0 \). - **Voltage Across Capacitor:** The voltage across the capacitor is denoted as \( v_c \). #### Additional Notes - The formula provided is used to calculate the voltage across the capacitor as a function of time \( t \). - \( v_c(\infty) \) represents the final steady-state voltage across the capacitor. - \( v_c(0^+) \) represents the initial voltage across the capacitor just after the switch is closed. - \( \tau \) (the time constant) is calculated based on the resistances and capacitance in the circuit.
Transcribed Image Text:### Transcription for Educational Use (b) After being opened for a long time, the switch in the circuit closes at \( t = 0 \). Compute \( v_c(t) \) for \( t \geq 0 \), where: \[ v_c(t) = v_c(\infty) + [v_c(0^+) - v_c(\infty)]e^{-\frac{t}{\tau}} \] #### Circuit Diagram Explanation - **Voltage Source:** There is a 5V voltage source in the circuit. - **Resistors:** Two resistors are present: - One with a resistance of 2Ω (ohms). - Another with a resistance of 3Ω (ohms). - **Capacitor:** A capacitor with a capacitance of 0.3μF (microfarads) is in the circuit. - **Switch:** The switch in the circuit closes at \( t = 0 \). - **Voltage Across Capacitor:** The voltage across the capacitor is denoted as \( v_c \). #### Additional Notes - The formula provided is used to calculate the voltage across the capacitor as a function of time \( t \). - \( v_c(\infty) \) represents the final steady-state voltage across the capacitor. - \( v_c(0^+) \) represents the initial voltage across the capacitor just after the switch is closed. - \( \tau \) (the time constant) is calculated based on the resistances and capacitance in the circuit.
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