A 400 Hz sinusoidal voltage with a maximum amplitude of 120 V at t = 0 is applied across the terminals of an inductor. The maximum amplitude of the steady-state current in the inductor is 20 A.
A 400 Hz sinusoidal voltage with a maximum amplitude of 120 V at t = 0 is applied across the terminals of an inductor. The maximum amplitude of the steady-state current in the inductor is 20 A.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![### Example Problem on Inductors and Sinusoidal Voltages
#### Given:
A 400 Hz sinusoidal voltage with a maximum amplitude of 120 V at \( t = 0 \) is applied across the terminals of an inductor. The maximum amplitude of the steady-state current in the inductor is 20 A.
#### Part C:
**Question:** What is the inductive reactance of the inductor?
**Instruction:** Express your answer with the appropriate units.
**Answer Format:**
\[ X_L = \_\_\_\_ \, \text{Units} \]
#### Part D:
**Question:** What is the inductance of the inductor?
**Instruction:** Express your answer with the appropriate units.
**Answer Format:**
\[ L = \_\_\_\_ \, \text{Units} \]
#### Explanation of Formulas and Steps to Solve:
1. **Calculate Inductive Reactance (\( X_L \))**:
\[
X_L = \frac{V_{\text{max}}}{I_{\text{max}}}
\]
Where \( V_{\text{max}} = 120 \text{ V} \) and \( I_{\text{max}} = 20 \text{ A} \).
\[
X_L = \frac{120 \text{ V}}{20 \text{ A}} = 6 \text{ Ω}
\]
2. **Calculate Inductance (\( L \))**:
\[
X_L = 2 \pi f L
\]
Where \( f = 400 \text{ Hz} \).
\[
L = \frac{X_L}{2 \pi f} = \frac{6 \text{ Ω}}{2 \pi \times 400 \text{ Hz}} \approx 2.39 \text{ mH}
\]
These solutions can be entered in the corresponding fields for evaluation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07dc3289-c262-41f1-9fc5-a8d18500de1b%2Fcf8dcf4d-697b-4e16-9a06-1a5ae016255c%2Fo42i4fe_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Problem on Inductors and Sinusoidal Voltages
#### Given:
A 400 Hz sinusoidal voltage with a maximum amplitude of 120 V at \( t = 0 \) is applied across the terminals of an inductor. The maximum amplitude of the steady-state current in the inductor is 20 A.
#### Part C:
**Question:** What is the inductive reactance of the inductor?
**Instruction:** Express your answer with the appropriate units.
**Answer Format:**
\[ X_L = \_\_\_\_ \, \text{Units} \]
#### Part D:
**Question:** What is the inductance of the inductor?
**Instruction:** Express your answer with the appropriate units.
**Answer Format:**
\[ L = \_\_\_\_ \, \text{Units} \]
#### Explanation of Formulas and Steps to Solve:
1. **Calculate Inductive Reactance (\( X_L \))**:
\[
X_L = \frac{V_{\text{max}}}{I_{\text{max}}}
\]
Where \( V_{\text{max}} = 120 \text{ V} \) and \( I_{\text{max}} = 20 \text{ A} \).
\[
X_L = \frac{120 \text{ V}}{20 \text{ A}} = 6 \text{ Ω}
\]
2. **Calculate Inductance (\( L \))**:
\[
X_L = 2 \pi f L
\]
Where \( f = 400 \text{ Hz} \).
\[
L = \frac{X_L}{2 \pi f} = \frac{6 \text{ Ω}}{2 \pi \times 400 \text{ Hz}} \approx 2.39 \text{ mH}
\]
These solutions can be entered in the corresponding fields for evaluation.
---
#### Part B:
**Question:** If the phase angle of the voltage is zero, what is the phase angle of the current?
**Instruction:** Express your answer with the appropriate units.
**Input:**
- A field to input the phase angle value.
- A drop-down to select the unit of the angle.
**Graphical/Diagram Explanation:**
- There is an input box for entering the value of the phase angle (θ) with a unit selector next to it. This field also supports formatting and symbols.
**Output:**
- Upon pressing "Submit," your answer will be validated.
](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07dc3289-c262-41f1-9fc5-a8d18500de1b%2Fcf8dcf4d-697b-4e16-9a06-1a5ae016255c%2Fkaheh59_processed.png&w=3840&q=75)
Transcribed Image Text:### Interactive Exercise: Inductor Current Analysis
This interactive problem is designed to test your understanding of sinusoidal voltages applied to inductors. Consider the scenario described below:
---
#### Problem Statement:
A 400 Hz sinusoidal voltage with a maximum amplitude of 120 V at \( t = 0 \) is applied across the terminals of an inductor. The maximum amplitude of the steady-state current in the inductor is 20 A.
---
#### Part A:
**Question:** What is the frequency of the inductor current?
**Instruction:** Express your answer with the appropriate units.
**Input:**
- A field to input the frequency value.
- A drop-down to select the unit of frequency.
**Graphical/Diagram Explanation:**
- There is an input box for entering the value of frequency (f) with a unit selector next to it. The input field is equipped with tools for formatting and symbols.
**Output:**
- Upon pressing "Submit," your answer will be validated.
---
#### Part B:
**Question:** If the phase angle of the voltage is zero, what is the phase angle of the current?
**Instruction:** Express your answer with the appropriate units.
**Input:**
- A field to input the phase angle value.
- A drop-down to select the unit of the angle.
**Graphical/Diagram Explanation:**
- There is an input box for entering the value of the phase angle (θ) with a unit selector next to it. This field also supports formatting and symbols.
**Output:**
- Upon pressing "Submit," your answer will be validated.
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