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Switch S1 has been closed and S2 has open for a long time until the capacitors are fully charged. At t=0, S1 is opened and S2 is closed. If x=12V, C₁=4mF and C₂=8mF, R₁=2.22k and R₂-2.57 k; what is the voltage on R₂ at t=0? Please express your answer using one decimal place. E R₁ www G S a {} b R₂

Switch S1 has been closed and S2 has open for a long time until the capacitors are fully charged. At t=0, S1 is opened and S2 is closed. If x=12V, C₁=4mF and C₂=8mF, R₁=2.22k and R₂-2.57 k; what is the voltage on R₂ at t=0? Please express your answer using one decimal place. E R₁ www G S a {} b R₂

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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### Problem Statement: Switch S1 has been closed and S2 has been open for a long time until the capacitors are fully charged. At t=0, S1 is opened and S2 is closed. If ε = 12V, C1 = 4mF, and C2 = 8mF, R1 = 2.22kΩ, and R2 = 2.57kΩ, what is the voltage on R2 at t=0? Please express your answer using one decimal place. ### Circuit Diagram Description: The given circuit diagram consists of two resistors (R1 and R2), two capacitors (C1 and C2), and two switches (S1 and S2). The battery provides an emf (ε) of 12V. The components are connected as follows: 1. **Battery (ε = 12V):** - Positive terminal connected to resistor R1 and switch S1. - Negative terminal connected to capacitor C2. 2. **Resistor R1 (2.22kΩ):** - Connected between the positive terminal of the battery and node a. 3. **Capacitor C1 (4mF):** - Connected between node a and node b where node b is also connected to the negative terminal of the battery. 4. **Switch S1:** - Positioned between the positive terminal of the battery and node a. It is initially closed, enabling the charging of the capacitors. 5. **Switch S2:** - Positioned between node a and resistor R2 and initially open. 6. **Capacitor C2 (8mF):** - Connected between node b and the negative terminal of the battery. 7. **Resistor R2 (2.57kΩ):** - Connected between node a and the node where S2 is connected, and ultimately the circuit loop closes through the negative terminal of the battery when S2 is closed. ### Explanation and Analysis: Before t=0, S1 is closed, and S2 is open, allowing capacitors C1 and C2 to fully charge. At t=0, S1 is opened (disconnecting the battery) and S2 is closed. We need to find the voltage across R2 at t=0. Since the capacitors were fully charged: - Voltage across C1 is equal to the battery voltage (12V).
Transcribed Image Text:### Problem Statement: Switch S1 has been closed and S2 has been open for a long time until the capacitors are fully charged. At t=0, S1 is opened and S2 is closed. If ε = 12V, C1 = 4mF, and C2 = 8mF, R1 = 2.22kΩ, and R2 = 2.57kΩ, what is the voltage on R2 at t=0? Please express your answer using one decimal place. ### Circuit Diagram Description: The given circuit diagram consists of two resistors (R1 and R2), two capacitors (C1 and C2), and two switches (S1 and S2). The battery provides an emf (ε) of 12V. The components are connected as follows: 1. **Battery (ε = 12V):** - Positive terminal connected to resistor R1 and switch S1. - Negative terminal connected to capacitor C2. 2. **Resistor R1 (2.22kΩ):** - Connected between the positive terminal of the battery and node a. 3. **Capacitor C1 (4mF):** - Connected between node a and node b where node b is also connected to the negative terminal of the battery. 4. **Switch S1:** - Positioned between the positive terminal of the battery and node a. It is initially closed, enabling the charging of the capacitors. 5. **Switch S2:** - Positioned between node a and resistor R2 and initially open. 6. **Capacitor C2 (8mF):** - Connected between node b and the negative terminal of the battery. 7. **Resistor R2 (2.57kΩ):** - Connected between node a and the node where S2 is connected, and ultimately the circuit loop closes through the negative terminal of the battery when S2 is closed. ### Explanation and Analysis: Before t=0, S1 is closed, and S2 is open, allowing capacitors C1 and C2 to fully charge. At t=0, S1 is opened (disconnecting the battery) and S2 is closed. We need to find the voltage across R2 at t=0. Since the capacitors were fully charged: - Voltage across C1 is equal to the battery voltage (12V).
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