To determine Find the value of i L ( 0 + ) in milliamperes for the given circuit. Explanation Given data: Refer to Figure 8.1 in the textbook for the given circuit. The natural voltage response for t ≥ 0 is given as follows: v ( t ) = 3 e − 100 t + 3 e − 900 t V (1) L = ( 40 / 9 ) H C = 2.5 μ F Formula used: Write the expression for voltage response of parallel R L C circuit for t ≥ 0 as follows: v ( t ) = A 1 e s 1 t + A 2 e s 2 t , t ≥ 0 (2) Here, A 1 , A 2 are unknown constants and s 1 , s 2 are characteristic roots. Refer Table 8.1 in the textbook for Natural-Response parameters of parallel R L C circuit, and write the expression for characteristic root s 1 as follows: s 1 = − α + α 2 − ω 0 2 (3) Refer Table 8.1 in the textbook, and write the expression for characteristic root s 2 as follows: s 2 = − α − α 2 − ω 0 2 (4) Refer Table 8.1 in the textbook, and write the expression for neper frequency for parallel R L C circuit as follows: α = 1 2 R C (5) Here, R is the resistance of the resistor and C is the capacitance of the capacitor. Write the expression for i L ( t ) for t ≥ 0 + as follows: i L ( t ) = − [ i R ( t ) + i C ( t ) ] (6) Write the expression for i R ( t ) for t ≥ 0 + as follows: i R ( t ) = v ( t ) R (7) Write the expression for i C ( t ) for t ≥ 0 + as follows: i C ( t ) = C d d t [ v ( t ) ] (8) Calculation: Compare Equation (1) with Equation (2) and write the characteristic roots as follows: s 1 = − 100 s 2 = − 900 Substitute ( − 100 ) for s 1 in Equation (3) as follows: − 100 = − α + α 2 − ω 0 2 − α + α 2 − ω 0 2 = − 100 (9) Substitute ( − 900 ) for s 2 in Equation (4) as follows: − 900 = − α − α 2 − ω 0 2 − α − α 2 − ω 0 2 = − 900 (10) Add Equations (9) and (10) to obtain the value of α . ( − α + α 2 − ω 0 2 ) + ( − α − α 2 − ω 0 2 ) = − 100 + ( − 900 ) − 2 α = − 1000 α = 500 rad / s Rearrange the expression in Equation (5) as follows: R = 1 2 α C Substitute 500 rad / s for α and 2 .5 μ F for C to obtain the value of resistance of the resistor. R = 1 ( 2 ) ( 500 rad / s ) ( 2 .5 μ F ) = 1 ( 2 ) ( 500 ) ( 2 .5 × 10 − 6 ) Ω = 400 Ω Substitute 0 for t in Equation (1) to find the value of v ( 0 + )

11th Edition

ISBN: 8220106795262

Author: Riedel

Publisher: YUZU

See similar textbooks

Concept explainers

Wheatstone Bridge Method

A Wheatstone bridge is a circuit used to measure unknown resistance by measuring the ratios of the two branches of the circuit such that each branch has two resistance and out of four resistance one is unknown. The two branches are joined in between with…

Videos

Question

Chapter 8, Problem 7P

To determine

Find the value of iL(0+) in milliamperes for the given circuit.

Expert Solution & Answer

Chapter 8 Solutions

EBK ELECTRIC CIRCUITS

Ch. 8.1 - The resistance and inductance of the circuit in...Ch. 8.2 - Use the integral relationship between iL and v to...Ch. 8.2 - Prob. 3AP Ch. 8.2 - Prob. 4AP Ch. 8.2 - Prob. 5AP Ch. 8.3 - Prob. 6AP Ch. 8.4 - Prob. 7AP Ch. 8.4 - Prob. 8AP Ch. 8.4 - Repeat Assessment Problems 8.7 and 8.8 if the 80 Ω...Ch. 8 - The resistance, inductance, and capacitance in a...

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

SEE MORE QUESTIONS

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
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,

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,

SEE MORE TEXTBOOKS

ME32 Wheatstone Bridge Method; Author: Lectures in Electrical Engineering;https://www.youtube.com/watch?v=p8iTTpzMR38;License: Standard YouTube License, CC-BY