Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
For the circuit of Figure 4.8, determine voltages across R, L and C if the source is 7 volts RMS.
![### Problem Statement
Determine the voltages across R, L, and C in the circuit of Figure 4.8, if the source voltage is 7 volts RMS.
### Circuit Description
The circuit in Figure 4.8 comprises:
- An AC voltage source E with a root mean square (RMS) value of 7 volts.
- A resistor (R) with a resistance of 100 ohms.
- An inductor (L) with an inductive reactance of \( j200 \) ohms.
- A capacitor (C) with a capacitive reactance of \( -j300 \) ohms.
### Circuit Diagram
The provided diagram (Figure 4.8) shows a simple AC circuit where:
- The voltage source \( E \) is connected to a ground (referenced as zero potential).
- The components are connected in series, starting with the voltage source, followed by the inductor \( j200 \), then the resistor (R) with a value of 100 ohms, and finally, the capacitor with a reactance of \( -j300 \).
### Solution Explanation
To solve for the voltages across each component (R, L, and C), we will follow these steps:
1. **Determine Total Impedance (Z):**
- The impedance \( Z \) of the circuit is the sum of the individual impedances:
\[
Z = R + j\omega L + \frac{1}{j\omega C}
\]
- Substituting the given values: \( R = 100 \) ohms, \( j\omega L = j200 \) ohms, \( \frac{1}{j\omega C} = -j300 \) ohms,
\[
Z = 100 + j200 - j300 = 100 - j100 \text{ ohms}
\]
2. **Calculate the Current (I):**
- Using Ohm’s Law, \( V = IZ \), the current \( I \) is given by:
\[
I = \frac{V}{Z} = \frac{7}{100 - j100} \text{ A}
\]
- Converting \( Z \) to polar form for easier calculation:
\[
|Z| = \sqrt{(100)^2 + (-100)^2} = \sqrt{20000} =](https://content.bartleby.com/qna-images/question/5842debd-c7e0-436d-83d9-66a4971dddbf/fbcb41f0-c4f5-4fb7-8042-44c4fc0ca104/l9qd91g_processed.png)
Transcribed Image Text:### Problem Statement
Determine the voltages across R, L, and C in the circuit of Figure 4.8, if the source voltage is 7 volts RMS.
### Circuit Description
The circuit in Figure 4.8 comprises:
- An AC voltage source E with a root mean square (RMS) value of 7 volts.
- A resistor (R) with a resistance of 100 ohms.
- An inductor (L) with an inductive reactance of \( j200 \) ohms.
- A capacitor (C) with a capacitive reactance of \( -j300 \) ohms.
### Circuit Diagram
The provided diagram (Figure 4.8) shows a simple AC circuit where:
- The voltage source \( E \) is connected to a ground (referenced as zero potential).
- The components are connected in series, starting with the voltage source, followed by the inductor \( j200 \), then the resistor (R) with a value of 100 ohms, and finally, the capacitor with a reactance of \( -j300 \).
### Solution Explanation
To solve for the voltages across each component (R, L, and C), we will follow these steps:
1. **Determine Total Impedance (Z):**
- The impedance \( Z \) of the circuit is the sum of the individual impedances:
\[
Z = R + j\omega L + \frac{1}{j\omega C}
\]
- Substituting the given values: \( R = 100 \) ohms, \( j\omega L = j200 \) ohms, \( \frac{1}{j\omega C} = -j300 \) ohms,
\[
Z = 100 + j200 - j300 = 100 - j100 \text{ ohms}
\]
2. **Calculate the Current (I):**
- Using Ohm’s Law, \( V = IZ \), the current \( I \) is given by:
\[
I = \frac{V}{Z} = \frac{7}{100 - j100} \text{ A}
\]
- Converting \( Z \) to polar form for easier calculation:
\[
|Z| = \sqrt{(100)^2 + (-100)^2} = \sqrt{20000} =
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 nowThis is a popular solution!
Step by stepSolved in 2 steps with 1 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.Similar questions
- In reference to the load how are inductors connected to help prevent voltage spikes and surges?arrow_forwardAnother name for the RMS value of current or voltage is ... O the effective value O the exact value O the true value O the reactance valuearrow_forwardDetermine period, frequency and rms value of the plotted current waveforms. 1 } ((A) ((A) PT ro) 1...4.. A+arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSON
Delmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage Learning
Programmable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education 
Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill Education
Electric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSON
Engineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.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,