In the circuit shown below, the switch opens at t 0. Find the i1(t) for t > 0. %3D

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

Please answer question 8 with details on how to do it. Make handwriting legible please. Thank you.

**Transcription and Explanation for Educational Website**

---

**Problem Statement:**

8. In the circuit shown below, the switch opens at \( t = 0 \). Find the \( i_1(t) \) for \( t > 0 \).

**Circuit Description:**

- The circuit includes a voltage source of 12 V.
- There are two resistors in the circuit:
  - A 6 Ω resistor.
  - A 12 Ω resistor.
- An inductor with an inductance of 2 H.
- Initially, the switch is closed, but it opens at \( t = 0 \).
  
**Diagram Explanation:**

- The circuit diagram depicts a series connection when the switch is closed:
  - The 12 V source is connected in series with the 6 Ω resistor.
  - The 12 Ω resistor and the 2 H inductor are in series with each other and parallel to the 6 Ω resistor.
- The current \( i_1(t) \) flows clockwise through the circuit branches.

**Task:**

- Find the current \( i_1(t) \) for \( t > 0 \).

**Hint for Solving:**

- Calculate \( i_1(t) \) at \( t < 0 \) first, which represents the steady state before the switch opens. This will help in finding the discharge current for the inductor for \( t > 0 \).

Given the circuit elements and initial conditions, applying Kirchhoff’s laws and the principles of an RL (Resistor-Inductor) circuit will help in solving for \( i_1(t) \).

--- 

This explanation provides a clear understanding of the circuit and its conditions for learners seeking to solve for the current through the circuit components as time progresses past the opening of the switch.
Transcribed Image Text:**Transcription and Explanation for Educational Website** --- **Problem Statement:** 8. In the circuit shown below, the switch opens at \( t = 0 \). Find the \( i_1(t) \) for \( t > 0 \). **Circuit Description:** - The circuit includes a voltage source of 12 V. - There are two resistors in the circuit: - A 6 Ω resistor. - A 12 Ω resistor. - An inductor with an inductance of 2 H. - Initially, the switch is closed, but it opens at \( t = 0 \). **Diagram Explanation:** - The circuit diagram depicts a series connection when the switch is closed: - The 12 V source is connected in series with the 6 Ω resistor. - The 12 Ω resistor and the 2 H inductor are in series with each other and parallel to the 6 Ω resistor. - The current \( i_1(t) \) flows clockwise through the circuit branches. **Task:** - Find the current \( i_1(t) \) for \( t > 0 \). **Hint for Solving:** - Calculate \( i_1(t) \) at \( t < 0 \) first, which represents the steady state before the switch opens. This will help in finding the discharge current for the inductor for \( t > 0 \). Given the circuit elements and initial conditions, applying Kirchhoff’s laws and the principles of an RL (Resistor-Inductor) circuit will help in solving for \( i_1(t) \). --- This explanation provides a clear understanding of the circuit and its conditions for learners seeking to solve for the current through the circuit components as time progresses past the opening of the switch.
Expert Solution
Step 1

Electrical Engineering homework question answer, step 1, image 1

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Similar 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,