Determine the power factor of the entire circuit below as seen by the source. Calculate the average power delivered by the source. -j22 3020° Vrms
Determine the power factor of the entire circuit below as seen by the source. Calculate the average power delivered by the source. -j22 3020° Vrms
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...
Related questions
Question
question is in the image
![**Problem Statement:**
Determine the power factor of the entire circuit below as seen by the source. Calculate the average power delivered by the source.
**Circuit Diagram:**
The circuit consists of the following components:
1. An AC voltage source of \(30 \angle 0^\circ \, V_{rms}\)
2. A series resistor of \(6 \Omega\)
3. A parallel combination of:
- Capacitive reactance of \(-j2 \Omega\)
- A resistor of \(4 \Omega\)
**Detailed Description of the Circuit:**
- The voltage source is represented by a sinusoidal symbol.
- The series resistor has a resistance of \(6 \Omega\).
- The parallel combination follows after the \(6 \Omega\) resistor and consists of:
- A capacitor with a capacitive reactance of \(-j2 \Omega\) (indicating a reactive component with \( \text{Capacitive reactance} = \frac{1}{\omega C} \))
- A resistor with a resistance of \(4 \Omega\)
**Task:**
1. **Determine the Power Factor:**
- The power factor of an electrical circuit is a measure of how effectively the current is being converted into useful work power and is defined as the ratio of real power to apparent power.
2. **Calculate the Average Power Delivered by the Source:**
- The average power (also known as real power) delivered by the source is calculated using the formula:
\[
P = V_{rms} \cdot I_{rms} \cdot \cos(\phi)
\]
where \(\phi\) is the phase angle between the voltage and the current.
**Note:**
To solve this problem, take the following steps:
- Determine the equivalent impedance of the circuit as seen by the source.
- Calculate the current flowing through the circuit using Ohm's Law.
- Compute the power factor.
- Calculate the average power delivered by the source.
**Explanation of Diagram:**
The circuit diagram shows an AC voltage source connected in series with a 6-ohm resistor. This series connection is then in parallel with a 4-ohm resistor and a capacitive reactance of -j2 ohms. The components are connected as follows:
1. The voltage source symbol is at the leftmost part, with the magnitude and phase angle denoted as \(30 \angle](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F755354d9-56be-4d3a-9cd7-bb7b08867ede%2F364a725f-29d6-4ead-9681-5395274ba45e%2Fus9p6pe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine the power factor of the entire circuit below as seen by the source. Calculate the average power delivered by the source.
**Circuit Diagram:**
The circuit consists of the following components:
1. An AC voltage source of \(30 \angle 0^\circ \, V_{rms}\)
2. A series resistor of \(6 \Omega\)
3. A parallel combination of:
- Capacitive reactance of \(-j2 \Omega\)
- A resistor of \(4 \Omega\)
**Detailed Description of the Circuit:**
- The voltage source is represented by a sinusoidal symbol.
- The series resistor has a resistance of \(6 \Omega\).
- The parallel combination follows after the \(6 \Omega\) resistor and consists of:
- A capacitor with a capacitive reactance of \(-j2 \Omega\) (indicating a reactive component with \( \text{Capacitive reactance} = \frac{1}{\omega C} \))
- A resistor with a resistance of \(4 \Omega\)
**Task:**
1. **Determine the Power Factor:**
- The power factor of an electrical circuit is a measure of how effectively the current is being converted into useful work power and is defined as the ratio of real power to apparent power.
2. **Calculate the Average Power Delivered by the Source:**
- The average power (also known as real power) delivered by the source is calculated using the formula:
\[
P = V_{rms} \cdot I_{rms} \cdot \cos(\phi)
\]
where \(\phi\) is the phase angle between the voltage and the current.
**Note:**
To solve this problem, take the following steps:
- Determine the equivalent impedance of the circuit as seen by the source.
- Calculate the current flowing through the circuit using Ohm's Law.
- Compute the power factor.
- Calculate the average power delivered by the source.
**Explanation of Diagram:**
The circuit diagram shows an AC voltage source connected in series with a 6-ohm resistor. This series connection is then in parallel with a 4-ohm resistor and a capacitive reactance of -j2 ohms. The components are connected as follows:
1. The voltage source symbol is at the leftmost part, with the magnitude and phase angle denoted as \(30 \angle
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
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.Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,