ECE201 Lect-171 Capacitors (6.1); Inductors (6.2); LC Combinations (6.3) Dr. Holbert April 5, 2006.
Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1...
Transcript of Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1...
![Page 1: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/1.jpg)
Chapter 8 Basic RL and RC Circuits
Engineering Circuit Analysis Sixth EditionW.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin
Copyright © 2002 McGraw-Hill, Inc. All Rights Reserved.
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Fig. 8.1 A series RL circuit for which i(t) is to be determined…Fig. 8.6 A plot of the exponential response versus time..
Fig. 8.11 A parallel RC circuit for which v(t) is to be determined...
Fig. 8.21 (a) A voltage-step function is shown as the source...
Fig. 8.19 (and Fig. 8.20) Two versions of the unit-step function…
Fig. 8.23 A useful forcing function, the rectangular voltage pulse.
Figs. 8.29 (and 8.30) Circuit from Example 8.4.
Fig. 8.31 (and 8.32) Circuit from Example 8.5..
Fig. 8.34 Circuit for Example 8.6.
![Page 2: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/2.jpg)
Fig. 8.1 A series RL circuitfor which i(t) is to bedetermined, subject to theinitial condition that I(0) = I0.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
A series RL circuit for which i(t)is to be determined, subject tothe initial condition that i(0) = I0.
KVL: R i t( ) + L ddt
i t( )( ) = 0
1st-order, linear, constant-coefficient, ordinary, homogeneousdifferential equation. The solution form is i t( ) = Ae!t .
RAe!t + L!Ae!t = 0" R + !L = 0"! = #R / L " i t( ) = Ae#Rt / L .
To find A we need a boundary condition. The most common boundary condition is i 0( ) = I0. Then
I0 = A" i t( ) = I0e#Rt / L
![Page 3: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/3.jpg)
Fig. 8.6 A plot of theexponential responseversus time.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
A plot of the exponential response versus time.
i t( ) = I0e!Rt / L = I0e
! t /" where " = L / R
![Page 4: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/4.jpg)
Fig. 8.11 A parallel RCcircuit for which v(t) is tobe determined, subject tothe initial condition thatv(0) = V0.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
A parallel RC circuit for whichv(t) is to be determined,subject to the initial conditionthat v(0) = V0.
KCL: C ddt
v t( )( ) + v t( )R
= 0 , v t( ) = Ae!t "CA!e!t + Ae!t
R= 0
C! +1/ R = 0"! = #1/ RC " v t( ) = Ae# t / RC
If v 0( ) =V0 , then v t( ) =V0e# t / RC =V0e
# t /$ , where $ = RC.
![Page 5: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/5.jpg)
Fig. 8.21 (a) A voltage-stepfunction is shown as the sourcedriving a general network.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
(a) A voltage-step forcing function is shown as the source driving ageneral network. (b) A simple circuit which, although not the exactequivalent of part (a), may be used as its equivalent in many cases.(c) An exact equivalent of part (a).
![Page 6: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/6.jpg)
Fig. 8.19 and Fig. 8.20 Twoversions of the unit-step forcingfunction.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
The unit-step forcingfunction u(t – t0).
The unit-step forcingfunction u(t).
![Page 7: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/7.jpg)
Fig. 8.23 A useful forcingfunction, the rectangularvoltage pulse.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
The rectangular pulsefunction
!"
!#$
><<
<=%
tt ttt
ttttv
1
100
0
0
0 V
0 )(
![Page 8: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/8.jpg)
Driven RL Circuit
R i t( ) + L ddt
i t( )( ) =Vs u t( )Solution form is i t( ) = Ae! t /" + I f , t > 0 where I f = i #( ). " = L / R , I f =Vs / R $ i t( ) = Ae!Rt / L +Vs / R
i 0+( ) = i 0!( ) = 0 = A+Vs / R $ A = !Vs / R
i t( ) = Vs / R( ) 1! e!Rt / L( ) , t > 0
![Page 9: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/9.jpg)
Driven RC Circuit
v t( )
R+C d
dtv t( )( ) = Is u t( )
Solution form is v t( ) = Ae! t /" +Vf , t > 0 where Vf = v #( ). " = RC , Vf = RIs $ v t( ) = Ae! t / RC + RIs
v 0+( ) = v 0!( ) = 0 = A+ RIs $ A = !RIs
v t( ) = RIs 1! e! t / RC( ) , t > 0
![Page 10: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/10.jpg)
Figs. 8.29 and 8.30 Circuitfrom Example 8.4.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
Circuit for which acomplete response i(t) isdesired.
The desired currentresponse as a function oftime.
![Page 11: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/11.jpg)
Fig. 8.31 and 8.32 Circuitfrom Example 8.5.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
(c) (d)
(a) Pulse waveform; (b) Circuit driven by waveform (a); (c) ! = t0/2; (d) ! = 2t0.
![Page 12: Chapter 8 Basic RL and RC Circuitsweb.eecs.utk.edu/~mjr/ECE201/PresentationSlides/chapter...Fig. 8.1 A series RL circuit for which i(t) is to be determined… Fig. 8.6 A plot of the](https://reader031.fdocuments.us/reader031/viewer/2022021605/5e6b159394a23b743b2a6177/html5/thumbnails/12.jpg)
Fig. 8.34 Circuit for Example8.6.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
Find the capacitor voltage vC(t) and the current i(t) in the 200-"resistor of the circuit shown in (a).
(a) Original circuit; (b) circuit valid for t # 0; (c) circuit for t $ 0.