### 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:**\[ X_L = \_\_\_\_ \, \text{Units} \]![Input Field Interface](http://example.com/image.png)#### Part D:**Question:** What is the inductance of the inductor?**Instruction:** Express your answer with the appropriate units.**Answer Format:**\[ L = \_\_\_\_ \, \text{Units} \]![Input Field Interface](http://example.com/image.png)#### 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. ### Interactive Exercise: Inductor Current AnalysisThis 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.![Frequency Input](https://i.imgur.com/GPd2XAi.png)---#### 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.![Phase Angle Input](https://i.imgur.com/xYN3NT0.png)

Answered: Image /qna-images/answer/cf8dcf4d-697b-4e16-9a06-1a5ae016255c.jpg

Answered: A 400 Hz sinusoidal voltage with 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)

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...

See similar textbooks

Related questions

Q: 6. The current in a 24-mH inductor is given by the waveform in the figure below. Find the waveform…

A: In this question we need to draw a waveform for the voltage across inductor.

Q: What will be the impedance of an inductor of inductancs 4 mH? The ac input frequency is 50 Hz.

A: If an inductor of the inductance of L H is subjected to ac of input frequency of f Hz, then the…

Q: An inductor and a capacitor are connected to a power system with the frequency of 55 Hz in parallel.…

A: We are given that an inductor and a caacitor are connected to a power system with the frequency of…

Q: As a capacitor charges, the current through it: rises according to the time constant. lags behind…

A: The question is asking about the behavior of the current through a capacitor as it charges. This…

Q: A sinusoidal current of amplitude 10 A and frequency of 10 kHz is applied and allowed to flow…

A: If i(t) A is the time varying current flowing through an inductor of inductance L H, then the…

Q: What is the capacitive reactance of a 1000-F capacitor at 60 Hz? And what is the current flow…

Q: Whenever current in an inductor changes: Select one: the coil inductance changes. induced voltage…

A: The objective of the question is to understand the behavior of an inductor when the current flowing…

Q: voltage of 34V RMS is applied across a real inductor. The current through the inductor is measured…

Q: 4.7 -mf capacitor is connected to a 60-Hz power source. What is the capacitive reactance of the…

A: In this question , we have to find capacitive reactance...

Q: .What is the magnitude of the impedance of a 73 mH inductor? Assume the frequency is 430 Hz .Write…

A: In this question, We need to determine the magnitude of the impedance? If inductance L= 73mH and…

Q: The voltage on 3 mH inductor is shown in figure. Find and draw the * .current i UL 15.0 4 t, ms…

A: Voltage across an inductor of inductance 'L' is V=Ldidt

Q: OF: An Electric Utility supplies 7.2 kV to a customer whose load is 7.2 kV 1300 kVA @pf=0.3845…

Q: Select all correct statement(s): 1, The equivalent resistance for resistors in parallel is the…

Q: What is the inductance of a circuit containing two 10h inductors connected in parallel? A. 20 h. B.…

A: In this question we need to find the equivalent inductance and time constant for the given circuit

Q: Find L7 in the network in the figure (a) with the switch open and (b) with the switch closed. All…

Q: In the circuit shown in Figure, the switch S is closed at time t = 0. the voltage across the…

A: We need to find out the voltage across inductor

Q: 34. An inductor has an inductance of 200 mH and is connected in series with a 1 kΩ…

Q: The reactance of a capacitor drops as: Select one: voltage increases. current increases. the…

A: The magnitude of capacitance is given by the formula: XC=2πfC1where "f" is the frequency and "C"…

Question

100%

### 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:**
\[ X_L = \_\_\_\_ \, \text{Units} \]
![Input Field Interface](http://example.com/image.png)

#### Part D:
**Question:** What is the inductance of the inductor?

**Instruction:** Express your answer with the appropriate units.

**Answer Format:**
\[ L = \_\_\_\_ \, \text{Units} \]
![Input Field Interface](http://example.com/image.png)

#### 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.

### 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.

![Frequency Input](https://i.imgur.com/GPd2XAi.png)

---

#### 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.

![Phase Angle Input](https://i.imgur.com/xYN3NT0.png)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data :-

Step 2: Part (A):-

Step 3: Part (B):-

Step 4: Part (C):-

Step 5: Part (D):-

Solution

Step by step

Solved in 6 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

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

Suppose the voltage across the inductor is ΔvR = ΔVmax= RVmax sin wt Find the current through this inductor and draw the waveforms of both current and voltage Here R is equal to 4
Item : TLO #: TLO 1 A 100-mH inductor is connected in parallel to the series connection of a variable resistor R and a 20-uF capacitor. The circuit is energized by a 120 Vac, 60-Hz supply. Find the value of R such that the total circuit current is 2.3023054 - 86.6782 A.
Please answer in typing format
Q) Initial current across a capacitor connected across a DC source is huge and initial voltage is zero, explain why this is so? NOTE: Answer must not exceed more than 5 lines
i need the answer quickly
A 100-mH inductor is connected in parallel to the series connection of a variable resistor R and a 20-pF capacitor. The circuit is energized by a 120 Vac, 60-Hz supply. Find the value of R such that the total circuit current is 2.302305Z - 86.6782 A.
the equivalent impedance of a capacitor in parallel with an iductor is equivalent to an open circuit (i.e equal to infinity) at a certain frequency.Drive an expression for this frequency
A sinusoidal current of 1.5 Arms is flowing through a capacitor of capacitance 20 uF. Find the Voltage across the capacitor at a frequency of 250HZ. Select one: O a. 0.471 O b. 0.047 O. 47.746 O d. 0.181
Question 5 We have a 1 H inductor connected between the input and the output of a circuit with a gain of -100. We wish to replace this inductor with two new inductor: one across the input and one across the output. Find the values of these two new inductors using Miller's theorem. Show your calculations.
The current in a 24-mH inductor is given by the waveform in the figure below. Find the waveform for the voltage across the inductor.
6. What is the total capacitance of a circuit containing a .01 farad, a .015 farad, and a .001 farad capacitor, all connected in parallel? A. B. 035 farad. .06 farad. C. .026 farad. D. .0026 farad.
A circuit consists of an inductor and two capacitors all in series. The inductor has a resistance of 10Ω and an inductance of 159μH. The first capacitor has 200pF and the second is a variable capacitor with a wide capacitive range. This series circuit is connected to a 50mV sinusoidal supply of fixed frequency 1MHz. (i) What value of the variable capacitance will be required for a resonance condition (give the answer in pF)?