RC Circuit For the circuit shown in Fig. 2| find v(t) for t>0. Assume the switch has been on for long enough time. t=0 40 4V(+ 50Z 4 2V + 10V 20 v(t)= 4F

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...
icon
Related questions
Question
## RC Circuit

### Problem Statement

For the circuit shown in Fig. 2, find \( v(t) \) for \( t \geq 0 \). Assume the switch has been on for a long enough time.

### Circuit Schematic

Diagrams in electrical engineering often involve several components connected in a specific manner. Figure 2 depicted below is one such circuit that involves resistors, capacitors, voltage sources, and a switch:

```
        4Ω                     
    |----\/\/\----|                     
    |             |                     
   4V             |                     
   |             /                     
  ---           / 1Ω                     
 ---          /  -------| t=0  <--/                         
   |         /            |                     
  2Ω       /         10V  --------                     
  |       /            |               \| 5Ω                     
  |      /             |                /    |---/\/\/\--------10τ    \           
  \---|                          |                    /                      2V                  
^(     \ (           v(t)| 4F     ) )                               )
   |        \|      |/                          |                  ^
|------|      |                                        /                   |                   
                   \| )

```
### Components and Their Connections

- **Resistors:**
  - 4Ω resistor in series with a 2Ω resistor on the left side of the circuit.
  - 1Ω resistor connected in series following the switch.
  - 5Ω resistor in series with the 2V voltage source on the right side.
  
- **Capacitor:**
  - A 4F capacitor is connected in parallel with the 2Ω resistor and positioned across the switch.

- **Voltage Sources:**
  - A 4V voltage source connected in series with the 4Ω resistor.
  - A 10V voltage source connected in parallel with the 2V voltage source and the 5Ω resistor.

### Switch Operation

- The switch in the circuit opens at time \( t = 0 \). Before \( t = 0 \), the switch had been closed for enough time for the capacitor to reach a steady-state voltage.

### Objective

- Determine the voltage \( v(t) \) across the capacitor for \( t \geq 0 \) after the switch has been opened.

Understanding how these components interact will allow us to derive the voltage \( v(t) \) for the
Transcribed Image Text:## RC Circuit ### Problem Statement For the circuit shown in Fig. 2, find \( v(t) \) for \( t \geq 0 \). Assume the switch has been on for a long enough time. ### Circuit Schematic Diagrams in electrical engineering often involve several components connected in a specific manner. Figure 2 depicted below is one such circuit that involves resistors, capacitors, voltage sources, and a switch: ``` 4Ω |----\/\/\----| | | 4V | | / --- / 1Ω --- / -------| t=0 <--/ | / | 2Ω / 10V -------- | / | \| 5Ω | / | / |---/\/\/\--------10τ \ \---| | / 2V ^( \ ( v(t)| 4F ) ) ) | \| |/ | ^ |------| | / | \| ) ``` ### Components and Their Connections - **Resistors:** - 4Ω resistor in series with a 2Ω resistor on the left side of the circuit. - 1Ω resistor connected in series following the switch. - 5Ω resistor in series with the 2V voltage source on the right side. - **Capacitor:** - A 4F capacitor is connected in parallel with the 2Ω resistor and positioned across the switch. - **Voltage Sources:** - A 4V voltage source connected in series with the 4Ω resistor. - A 10V voltage source connected in parallel with the 2V voltage source and the 5Ω resistor. ### Switch Operation - The switch in the circuit opens at time \( t = 0 \). Before \( t = 0 \), the switch had been closed for enough time for the capacitor to reach a steady-state voltage. ### Objective - Determine the voltage \( v(t) \) across the capacitor for \( t \geq 0 \) after the switch has been opened. Understanding how these components interact will allow us to derive the voltage \( v(t) \) for the
Expert Solution
steps

Step by step

Solved in 4 steps with 7 images

Blurred answer
Knowledge Booster
Power Flow Analysis
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,