Consider the circuit shown below. R1 = 100 N R, = 100 N C, = 10 mF V = 12 V R3 3 100 N C, = 4.7 mF %D a. After the switch has been closed for a very long time, what are the voltages across the capacitors C and C2? Hint for (a) Voltage across C1 is V, and voltage across C2 is V. b. After the switch has been closed for a very long time, what is the energy stored in each capacitor? Hint for (b) Energy stored on C, is J, and energy stored on C2 is J.
Consider the circuit shown below. R1 = 100 N R, = 100 N C, = 10 mF V = 12 V R3 3 100 N C, = 4.7 mF %D a. After the switch has been closed for a very long time, what are the voltages across the capacitors C and C2? Hint for (a) Voltage across C1 is V, and voltage across C2 is V. b. After the switch has been closed for a very long time, what is the energy stored in each capacitor? Hint for (b) Energy stored on C, is J, and energy stored on C2 is J.
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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![### Circuit Analysis - Educational Exercise
**Circuit Diagram:**
The circuit consists of a series circuit with a voltage source \( V = 12 \, \text{V} \) connected to a resistor \( R_1 = 100 \, \Omega \), a capacitor \( C_1 = 10 \, \text{mF} \), a resistor \( R_2 = 100 \, \Omega \), another resistor \( R_3 = 100 \, \Omega \), and a capacitor \( C_2 = 4.7 \, \text{mF} \).
**Exercises:**
**a. Voltage Across the Capacitors:**
- After the switch has been closed for a very long time, determine the voltages across capacitors \( C_1 \) and \( C_2 \).
**Hint for (a):**
- Voltage across \( C_1 \) is \(\_\_\_\_\_\_\_\_\_\_ \) V, and voltage across \( C_2 \) is \(\_\_\_\_\_\_\_\_\_\_ \) V.
**b. Energy Stored in Each Capacitor:**
- After the switch has been closed for a very long time, calculate the energy stored in each capacitor.
**Hint for (b):**
- Energy stored on \( C_1 \) is \(\_\_\_\_\_\_\_\_\_\_ \) J, and energy stored on \( C_2 \) is \(\_\_\_\_\_\_\_\_\_\_ \) J.
**Explanation of Circuit:**
The circuit shows a standard configuration for analyzing the behavior of capacitors over a long period when connected to a DC voltage source. Initially, when the switch is closed, the capacitors start charging, and over time they reach steady-state conditions. At steady-state, the voltage across the capacitors can be calculated, and once known, the energy stored in them can also be determined using the formula:
\[ E = \frac{1}{2} C V^2 \]
where \( E \) is the energy, \( C \) is the capacitance, and \( V \) is the voltage across the capacitor.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe09d4462-f34d-4530-ac40-5ce52271c7b7%2Fdb9969b2-8d78-4a54-8f00-18b3b5a0eabc%2Frey2ch_processed.png&w=3840&q=75)
Transcribed Image Text:### Circuit Analysis - Educational Exercise
**Circuit Diagram:**
The circuit consists of a series circuit with a voltage source \( V = 12 \, \text{V} \) connected to a resistor \( R_1 = 100 \, \Omega \), a capacitor \( C_1 = 10 \, \text{mF} \), a resistor \( R_2 = 100 \, \Omega \), another resistor \( R_3 = 100 \, \Omega \), and a capacitor \( C_2 = 4.7 \, \text{mF} \).
**Exercises:**
**a. Voltage Across the Capacitors:**
- After the switch has been closed for a very long time, determine the voltages across capacitors \( C_1 \) and \( C_2 \).
**Hint for (a):**
- Voltage across \( C_1 \) is \(\_\_\_\_\_\_\_\_\_\_ \) V, and voltage across \( C_2 \) is \(\_\_\_\_\_\_\_\_\_\_ \) V.
**b. Energy Stored in Each Capacitor:**
- After the switch has been closed for a very long time, calculate the energy stored in each capacitor.
**Hint for (b):**
- Energy stored on \( C_1 \) is \(\_\_\_\_\_\_\_\_\_\_ \) J, and energy stored on \( C_2 \) is \(\_\_\_\_\_\_\_\_\_\_ \) J.
**Explanation of Circuit:**
The circuit shows a standard configuration for analyzing the behavior of capacitors over a long period when connected to a DC voltage source. Initially, when the switch is closed, the capacitors start charging, and over time they reach steady-state conditions. At steady-state, the voltage across the capacitors can be calculated, and once known, the energy stored in them can also be determined using the formula:
\[ E = \frac{1}{2} C V^2 \]
where \( E \) is the energy, \( C \) is the capacitance, and \( V \) is the voltage across the capacitor.
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