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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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The image shows a circuit diagram along with calculations to determine the voltage stored in a capacitor. Here's a detailed transcription and explanation: ### Circuit Diagram - The circuit is powered by a source voltage \( V_s \). - Three resistors \( R_1 \), \( R_2 \), and \( R_3 \) are connected within the circuit. - A capacitor is included and is represented by the symbol \( C \). - At time \( t = \infty \), the capacitor would be an open circuit when at maximum capacity. ### Given Values - Source Voltage \( V_s = 8V \) - Resistance \( R_1 = 100 \Omega \) - Resistance \( R_2 = 200 \Omega \) - Resistance \( R_3 = 300 \Omega \) - Capacitance \( C = 0.01 \text{ mF} \) - Voltage across the capacitor \( V_c = ? \) ### Key Points - The note stresses the need to find the voltage stored in the capacitor. - An equivalent resistance is given as \( R = 200 \Omega \). ### Calculations 1. **Current through the source:** \[ I_s = \frac{8}{600} = 0.0133 \text{ A} \] 2. **Voltage across \( R_2 \):** \[ V_s = \frac{8V}{220} = 0.036 \text{ A} \] 3. **Voltage across \( R_3 \):** \[ V_{R_3} = 3.6V \quad \text{and} \quad \frac{3.6}{300} = \text{Current calculation} = 0.012 \text{ A} \] This setup models a simple RC (resistor-capacitor) circuit. Understanding these calculations is crucial for analyzing circuits involving capacitors, especially for noting the behavior as the system reaches steady state (\( t = \infty \)).
Transcribed Image Text:The image shows a circuit diagram along with calculations to determine the voltage stored in a capacitor. Here's a detailed transcription and explanation: ### Circuit Diagram - The circuit is powered by a source voltage \( V_s \). - Three resistors \( R_1 \), \( R_2 \), and \( R_3 \) are connected within the circuit. - A capacitor is included and is represented by the symbol \( C \). - At time \( t = \infty \), the capacitor would be an open circuit when at maximum capacity. ### Given Values - Source Voltage \( V_s = 8V \) - Resistance \( R_1 = 100 \Omega \) - Resistance \( R_2 = 200 \Omega \) - Resistance \( R_3 = 300 \Omega \) - Capacitance \( C = 0.01 \text{ mF} \) - Voltage across the capacitor \( V_c = ? \) ### Key Points - The note stresses the need to find the voltage stored in the capacitor. - An equivalent resistance is given as \( R = 200 \Omega \). ### Calculations 1. **Current through the source:** \[ I_s = \frac{8}{600} = 0.0133 \text{ A} \] 2. **Voltage across \( R_2 \):** \[ V_s = \frac{8V}{220} = 0.036 \text{ A} \] 3. **Voltage across \( R_3 \):** \[ V_{R_3} = 3.6V \quad \text{and} \quad \frac{3.6}{300} = \text{Current calculation} = 0.012 \text{ A} \] This setup models a simple RC (resistor-capacitor) circuit. Understanding these calculations is crucial for analyzing circuits involving capacitors, especially for noting the behavior as the system reaches steady state (\( t = \infty \)).
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