The circuit below has fully adjusted. The switch is closed at t=0 s. Determine the expression for i(t) from t=0 to ∞ using the step-by-step method. Plot the solution and indicate the time for full response.
Sinusoids And Phasors
Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.
Circuit Theory
Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).
The circuit below has fully adjusted. The switch is closed at t=0 s. Determine the
expression for i(t) from t=0 to ∞ using the step-by-step method. Plot the solution and
indicate the time for full response.
![The image depicts an electrical circuit diagram consisting of resistors, inductors, and voltage sources. Here's a detailed description:
1. **Voltage Sources**:
- There is a 10 V voltage source connected in series with a 2 kΩ resistor. This source has its positive terminal connected upwards.
- Another 24 V voltage source is connected in series with a 6 kΩ resistor and a switch. The switch is labeled "t=0 s," indicating it closes at time zero.
2. **Resistors**:
- The first resistor (2 kΩ) is directly in series with the 10 V voltage source.
- The second resistor (6 kΩ) is in series with the 24 V source and the switch.
- A 3 kΩ resistor is connected in the horizontal branch of the circuit, in series with both voltage source loops.
3. **Inductors**:
- A 50 H inductor and a 100 H inductor are connected in series on the right side of the circuit.
4. **Current Indicator**:
- The current through the 2 kΩ resistor is labeled as i(t), with the direction of current flow indicated by an arrow pointing upwards.
The circuit exhibits a combination of resistive and inductive elements, providing a setup for analyzing transient and steady-state behavior in response to the switch closing at t=0. The analysis of this circuit can involve techniques from basic circuit theory, including Kirchhoff's laws, Thevenin's or Norton's theorems, and the Laplace transform for solving differential equations related to current and voltage over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff46f0681-7fa4-463e-82da-0ad16d039091%2Fd5b0977e-3158-424e-93dd-029d8fa64564%2F05rnc8c_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 4 steps with 5 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
![Fundamentals of Electric Circuits](https://www.bartleby.com/isbn_cover_images/9780078028229/9780078028229_smallCoverImage.gif)
![Electric Circuits. (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780134746968/9780134746968_smallCoverImage.gif)
![Engineering Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780078028151/9780078028151_smallCoverImage.gif)