Exercise 3) In the LRC circuit below, at time t = 0 the current in the inductor is io = 0.354 A. Avoltage is applied to the circuit at time t = ti sec and held constant until t = t2 sec before it is turnedoff, as shown on the right. Consider R = 1 N, L = 2 H and C = 0.5 F.RLv(t)A1v(t)Ctit2tWe wish to determine the current through the circuit i(t) considering the applied voltage v(t) andthe initial current in the inductor io using the Laplace transform. Follow the steps below.(a) Write the differential equation relating i(t) and v(t). At this time the values of t1 and t2 do notneed to be specified.(b) Take the Laplace transform of (a) considering the initial current in the inductor.(c) Solve for the current using the inverse Laplace transform.

Answered: Image /qna-images/answer/e320d528-f920-48e0-aa5c-eee01966f1d2.jpg

Exercise 3) In the LRC circuit below, at time t = 0 the current in the inductor is io voltage is applied to the circuit at time t = ti sec and held constant until t = t2 sec before it is off, as shown on the right. Consider R = 1 N, L = 2 H and C = 0.5 F. 0.354 R L v(t)A 1 v(t) C ti t2 t We wish to determine the current through the circuit i(t) considering the applied voltage v( the initial current in the inductor io using the Laplace transform. Follow the steps below. (a) Write the differential equation relating i(t) and v(t). At this time the values of t1 and t2 need to be specified. (b) Take the Laplace transform of (a) considering the initial current in the inductor. (c) Solve for the current using the inverse Laplace transform.

Exercise 3) In the LRC circuit below, at time t = 0 the current in the inductor is io voltage is applied to the circuit at time t = ti sec and held constant until t = t2 sec before it is off, as shown on the right. Consider R = 1 N, L = 2 H and C = 0.5 F. 0.354 R L v(t)A 1 v(t) C ti t2 t We wish to determine the current through the circuit i(t) considering the applied voltage v( the initial current in the inductor io using the Laplace transform. Follow the steps below. (a) Write the differential equation relating i(t) and v(t). At this time the values of t1 and t2 need to be specified. (b) Take the Laplace transform of (a) considering the initial current in the inductor. (c) Solve for the current using the inverse Laplace transform.

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...

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Concept explainers

Sinusoids And Phasors

Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.

Circuit Theory

Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).

Question

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Exercise 3) In the LRC circuit below, at time t = 0 the current in the inductor is io = 0.354 A. A
voltage is applied to the circuit at time t = ti sec and held constant until t = t2 sec before it is turned
off, as shown on the right. Consider R = 1 N, L = 2 H and C = 0.5 F.
R
L
v(t)A
1
v(t)
C
ti
t2
t
We wish to determine the current through the circuit i(t) considering the applied voltage v(t) and
the initial current in the inductor io using the Laplace transform. Follow the steps below.
(a) Write the differential equation relating i(t) and v(t). At this time the values of t1 and t2 do not
need to be specified.
(b) Take the Laplace transform of (a) considering the initial current in the inductor.
(c) Solve for the current using the inverse Laplace transform.

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