Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
A series RLC circuit contains a 4-kO resistor, an inductor with an inductive reactance (X,) of 3.5 kN, and a capacitor with a capacitive reactance (Xc) of 2.4 kN. A 120-Vac, 60-Hz power source is connected to the circuit. How much voltage is dropped across the inductor?

A series RLC circuit contains a 4-kO resistor, an inductor with an inductive reactance (X,) of 3.5 kN, and a capacitor with a capacitive reactance (Xc) of 2.4 kN. A 120-Vac, 60-Hz power source is connected to the circuit. How much voltage is dropped across the inductor?

Introductory Circuit Analysis (13th Edition)
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
icon
Related questions
Question
**RLC Circuit Voltage Drop Calculation** --- In this example, we analyze a series RLC circuit consisting of different electrical components and determine the voltage drop across the inductor. **Components and Given Values:** - **Resistor (R):** 4 kilo-ohms (kΩ). - **Inductor with Inductive Reactance (XL):** 3.5 kilo-ohms (kΩ). - **Capacitor with Capacitive Reactance (XC):** 2.4 kilo-ohms (kΩ). - **Power Source:** 120 volts AC (Vac), 60 hertz (Hz). **Problem Statement:** A series RLC circuit contains a 4-kΩ resistor, an inductor with an inductive reactance (XL) of 3.5 kΩ, and a capacitor with a capacitive reactance (XC) of 2.4 kΩ. A 120-Vac, 60-Hz power source is connected to the circuit. How much voltage is dropped across the inductor? **Solution:** 1. **Calculate the Impedance (Z) of the Circuit:** - The impedance, \( Z \), in a series RLC circuit is determined as: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] - Substituting the values: \[ Z = \sqrt{(4000)^2 + (3500 - 2400)^2} = \sqrt{(4000)^2 + (1100)^2} = \sqrt{16000000 + 1210000} = \sqrt{17210000} \approx 4148 \text{ ohms} \] 2. **Calculate the Current (I) in the Circuit:** - The current, \( I \), through the series circuit is determined by Ohm's law using the total voltage (V) and impedance (Z): \[ I = \frac{V}{Z} = \frac{120}{4148} \approx 0.0289 \text{ amps (A)} \] 3. **Calculate the Voltage Drop across the Inductor (V_L):** - The voltage drop across the inductor is given by: \[ V_L = I \times X_L \] - Substituting the values: \
Transcribed Image Text:**RLC Circuit Voltage Drop Calculation** --- In this example, we analyze a series RLC circuit consisting of different electrical components and determine the voltage drop across the inductor. **Components and Given Values:** - **Resistor (R):** 4 kilo-ohms (kΩ). - **Inductor with Inductive Reactance (XL):** 3.5 kilo-ohms (kΩ). - **Capacitor with Capacitive Reactance (XC):** 2.4 kilo-ohms (kΩ). - **Power Source:** 120 volts AC (Vac), 60 hertz (Hz). **Problem Statement:** A series RLC circuit contains a 4-kΩ resistor, an inductor with an inductive reactance (XL) of 3.5 kΩ, and a capacitor with a capacitive reactance (XC) of 2.4 kΩ. A 120-Vac, 60-Hz power source is connected to the circuit. How much voltage is dropped across the inductor? **Solution:** 1. **Calculate the Impedance (Z) of the Circuit:** - The impedance, \( Z \), in a series RLC circuit is determined as: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] - Substituting the values: \[ Z = \sqrt{(4000)^2 + (3500 - 2400)^2} = \sqrt{(4000)^2 + (1100)^2} = \sqrt{16000000 + 1210000} = \sqrt{17210000} \approx 4148 \text{ ohms} \] 2. **Calculate the Current (I) in the Circuit:** - The current, \( I \), through the series circuit is determined by Ohm's law using the total voltage (V) and impedance (Z): \[ I = \frac{V}{Z} = \frac{120}{4148} \approx 0.0289 \text{ amps (A)} \] 3. **Calculate the Voltage Drop across the Inductor (V_L):** - The voltage drop across the inductor is given by: \[ V_L = I \times X_L \] - Substituting the values: \
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Capacitor
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
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS