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What is the value of the time constant in the following cireuit? 133.1 mF 18 N + >132 v,(1) = -9 + 15u(t) v

What is the value of the time constant in the following cireuit? 133.1 mF 18 N + >132 v,(1) = -9 + 15u(t) v

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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**Question:** What is the value of the time constant in the following circuit? **Circuit Description:** The circuit consists of: - A voltage source defined by the function \( v_s(t) = -9 + 15u(t) \) V, where \( u(t) \) is the unit step function. - A capacitor with a capacitance of 133.1 mF. - Two resistors: - An 18 Ω resistor connected in series with the capacitor. - A 13 Ω resistor connected in parallel with the series combination of the capacitor and the 18 Ω resistor. **Labeling:** - Voltage across the capacitor is denoted as \( v_a \) (green). - Voltage across the 13 Ω resistor is denoted as \( v_o \) (purple). To find the time constant (\(\tau\)) of the circuit, use the formula: \[ \tau = R_{\text{eq}} \cdot C \] Where: - \( R_{\text{eq}} \) is the equivalent resistance seen by the capacitor. - \( C \) is the capacitance. In this circuit, calculate the equivalent resistance considering the arrangement of the resistors.
Transcribed Image Text:**Question:** What is the value of the time constant in the following circuit? **Circuit Description:** The circuit consists of: - A voltage source defined by the function \( v_s(t) = -9 + 15u(t) \) V, where \( u(t) \) is the unit step function. - A capacitor with a capacitance of 133.1 mF. - Two resistors: - An 18 Ω resistor connected in series with the capacitor. - A 13 Ω resistor connected in parallel with the series combination of the capacitor and the 18 Ω resistor. **Labeling:** - Voltage across the capacitor is denoted as \( v_a \) (green). - Voltage across the 13 Ω resistor is denoted as \( v_o \) (purple). To find the time constant (\(\tau\)) of the circuit, use the formula: \[ \tau = R_{\text{eq}} \cdot C \] Where: - \( R_{\text{eq}} \) is the equivalent resistance seen by the capacitor. - \( C \) is the capacitance. In this circuit, calculate the equivalent resistance considering the arrangement of the resistors.
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