Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![### Electrical Engineering Problem
---
#### Context:
The current in the circuit in the following figure is known to be:
\[ i = B_1 e^{-2000t} \cos 1500t + B_2 e^{-2000t} \sin 1500t, \quad t \geq 0. \]
The capacitor has a value of \(80 \, \text{nF}\) (nanofarads); the initial value of the current is \(9 \, \text{mA}\); and the initial voltage on the capacitor is \(-33 \, \text{V}\).
---
#### Circuit Diagram:
**Figure 1**
The circuit includes:
- A resistor \( R \)
- An inductor \( L \)
- A capacitor \( C \)
The diagram shows a series circuit with the inductor on the left, followed by the resistor, and the capacitor on the right. Current \( i(t) \) flows clockwise through the circuit, the voltage across the capacitor is denoted as \( V_0 \), and the inductor has an initial current \( I_0 \).
(Insert figure here.)
---
#### Interactive Problems:
---
**Part A**
**Find the value of \( R \).**
**Input Box:**
\[ R = \_\_\_\_ \, \text{units} \]
**Example Input:**
\[ R = 2 \, H \]
**Feedback:**
\[ \text{Incorrect; Try Again} \]
---
**Part B**
**Find the value of \( L \).**
**Input Box:**
\[ L = \_\_\_\_ \, \text{units} \]
(Note: Fill the appropriate value in the box and specify the units.)
---
#### Analysis and Explanation:
To solve for \( R \) and \( L \), we need to use the given initial conditions and solve the differential equations governing the circuit. Following steps should be included in the educational content:
1. **Identify the initial conditions**:
- Initial current (\( i(0) = 9 \, \text{mA} \)).
- Initial voltage across the capacitor (\( V_C(0) = -33 \, \text{V} \)).
2. **Formulate the system of differential equations** using Kirchhoff's laws.
3. **Solve the differential equations**:
- Typically involves finding the characteristic equation and the](https://content.bartleby.com/qna-images/question/d20dfe5a-a4c1-4793-9f05-a80ad59a67d4/69422031-e0e9-41d2-80b8-8f40149e1868/92ijvhw_processed.png)
Transcribed Image Text:### Electrical Engineering Problem
---
#### Context:
The current in the circuit in the following figure is known to be:
\[ i = B_1 e^{-2000t} \cos 1500t + B_2 e^{-2000t} \sin 1500t, \quad t \geq 0. \]
The capacitor has a value of \(80 \, \text{nF}\) (nanofarads); the initial value of the current is \(9 \, \text{mA}\); and the initial voltage on the capacitor is \(-33 \, \text{V}\).
---
#### Circuit Diagram:
**Figure 1**
The circuit includes:
- A resistor \( R \)
- An inductor \( L \)
- A capacitor \( C \)
The diagram shows a series circuit with the inductor on the left, followed by the resistor, and the capacitor on the right. Current \( i(t) \) flows clockwise through the circuit, the voltage across the capacitor is denoted as \( V_0 \), and the inductor has an initial current \( I_0 \).
(Insert figure here.)
---
#### Interactive Problems:
---
**Part A**
**Find the value of \( R \).**
**Input Box:**
\[ R = \_\_\_\_ \, \text{units} \]
**Example Input:**
\[ R = 2 \, H \]
**Feedback:**
\[ \text{Incorrect; Try Again} \]
---
**Part B**
**Find the value of \( L \).**
**Input Box:**
\[ L = \_\_\_\_ \, \text{units} \]
(Note: Fill the appropriate value in the box and specify the units.)
---
#### Analysis and Explanation:
To solve for \( R \) and \( L \), we need to use the given initial conditions and solve the differential equations governing the circuit. Following steps should be included in the educational content:
1. **Identify the initial conditions**:
- Initial current (\( i(0) = 9 \, \text{mA} \)).
- Initial voltage across the capacitor (\( V_C(0) = -33 \, \text{V} \)).
2. **Formulate the system of differential equations** using Kirchhoff's laws.
3. **Solve the differential equations**:
- Typically involves finding the characteristic equation and the
![### Part C
#### Find the value of \( B_1 \).
**Express your answer with the appropriate units.**
Below is the input box where you can enter the value and the unit for \( B_1 \):
\[ B_1 = \text{Value} \quad \text{Units} \]
There are also icons for various functionalities:
- **Calculator Icon**: To access a built-in calculator.
- **Mu Symbol (μA)**: Suggests microamperes as a potential unit.
- **Reset Icon**: To clear the input.
- **Undo Icon**: To revert the last action.
- **Question Mark**: For help or additional information.
After entering the value and unit, click the blue "Submit" button. There is also an option to "Request Answer" below the input box.
### Part D
#### Find the value of \( B_2 \).
**Express your answer with the appropriate units.**
In this part, the value of \( B_2 \) has already been provided as \( 0.7 \, \text{mA} \):
\[ B_2 = 0.7 \, \text{mA} \]
Similar to Part C, there are icons for:
- **Calculator Icon**
- **Mu Symbol (μA)**
- **Reset Icon**
- **Undo Icon**
- **Question Mark**
To proceed, simply click the blue "Submit" button below the pre-filled input box. Additionally, options for "Previous Answers" and "Request Answer" are available for further assistance.](https://content.bartleby.com/qna-images/question/d20dfe5a-a4c1-4793-9f05-a80ad59a67d4/69422031-e0e9-41d2-80b8-8f40149e1868/cqhembe_processed.png)
Transcribed Image Text:### Part C
#### Find the value of \( B_1 \).
**Express your answer with the appropriate units.**
Below is the input box where you can enter the value and the unit for \( B_1 \):
\[ B_1 = \text{Value} \quad \text{Units} \]
There are also icons for various functionalities:
- **Calculator Icon**: To access a built-in calculator.
- **Mu Symbol (μA)**: Suggests microamperes as a potential unit.
- **Reset Icon**: To clear the input.
- **Undo Icon**: To revert the last action.
- **Question Mark**: For help or additional information.
After entering the value and unit, click the blue "Submit" button. There is also an option to "Request Answer" below the input box.
### Part D
#### Find the value of \( B_2 \).
**Express your answer with the appropriate units.**
In this part, the value of \( B_2 \) has already been provided as \( 0.7 \, \text{mA} \):
\[ B_2 = 0.7 \, \text{mA} \]
Similar to Part C, there are icons for:
- **Calculator Icon**
- **Mu Symbol (μA)**
- **Reset Icon**
- **Undo Icon**
- **Question Mark**
To proceed, simply click the blue "Submit" button below the pre-filled input box. Additionally, options for "Previous Answers" and "Request Answer" are available for further assistance.
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