Segundo Orden
8
PROBLEMS 367 7.66 For th e netw ork in Fig. P7.6 6, choose C so th e lime con sta nt will be 1 20 L S f or I > O. t= 0 4 kO Vs 23 kO 18 kO Figure p] 66 7.67 Th e di ffere ntial e quat i on that d esc rib es the current i l in a network is d i o (t) di,,{l ) - + 6 + 4i o l ) = 0 dr dt Find (a) t he c haracteri s ti c equation of t he ne twork , (b) th e n e tw o rk s natural frequencie s, and c) th e expre ss i o n fori,, I). 7 . 6 8 The termina l curre nt in a network is described by th e equation ,I io ( l ) di , ( I ) + 8 - - + 16i { l = 0 dr dl Find (a) th e characteris ti c equation o f the network , ( b) th e network s natu ra l frequencies, and c) the eq ua ti o n for i ,,{ I ). 7 . 69 T h e vo lt age I t ) in a n e tw o rk is defin e d by the e quati o n d v ,( l ) dv,(t) - - + 4 + 5v ,(t) = 0 r dr Find a ) th e c hara c t e ri s tic equatio n o the n e twork , b) th e circuit s na t ura l fr eq ue n c i es, and (c ) th e expr es sion for v , t) . 7.70 The outp ut voltage of a circ u it is d esc ribed by th e diff e r- entia l eq uati o n d v o ( I ) dv o ( I ) - + 8 + 1 0 v.,{ l ) = 0 dt dt Find ( a ) th e c h aracter i stic e quati on of the circuit , ( b ) th e n e t wo rk s natura l frequenc i es, and (c) the eq uation f o r V ( I). C 7 · 71 Th e voltage vl{ t ) in a n et w ork i s de fined by t he equul i on d 1) ,(I ) [ dV,( I )] + 2 - - + 5v,(1) = 0 dl - dl Find (a) th e character i st ic equation of the n etwork. (b) the c ir cu i t s natural frequ e n cies. el th e expression for V,( I ) . 2kO C 0 + 7 kO Vo( I) 0 7 . 72 The parameter s for a parallel RLC cir c uit a r e R = I n , L = 1 / 2 H. and C = 1 / 2 F. Det e rmin e th e t ype of damping ex hibit ed by th e circuit. 7.73 A se rie s RLC c i rc ui t contain s a r es i s tor of R = 2 nand 0 a capac itor C = 1 / 2 F Sel ec t th e v alue of the induclOr s o t h at the circu it i s critica ll y damped. 7 . 74 A parall e l RLC c ir c uit contain s a re sist or I = I nand 0 a n indu ctor L = 2H. Se l ect th e v alu e of th e capacitor so that the c ircui t i s cr iti c a ll y damp e d. 7 . 75 For the underdamp ed circuit s ho w n in Fi g. P7.75 , 0 determin e the voltage v t ) if th e initial co ndi tion s o n the s torag e cl e m e nt s arc i JO) I A and v , O) = 1 0 V. 2H I Figure P].75 + + V(t) 5 0 1 vc O) 40 F 7 . 76 In th e cr iti ca ll y damped circuit s ho w n in Fig. P7.76. th e 0 initial co nditi on s on th e s torage cleme n ts ure i, . O = 2 A and v, O) = 5 V. Det e rmin e th e voltage v t ). + + vc o) r 001 F v t ) 100 r Figure P7 . 76 7.77 F in d . {t for t > 0 in th e c ircuit in Fig. P7 . 77 . ) t = 0 + 1 A 8 0 0.04 F Figure P7 77
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Transcript of Segundo Orden
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PROBLEMS 367
7.66 For the network in Fig. P7.66, choose C so the lime consta nt will be 120 I-L S for I > O.
t= 0 4 kO
Vs 23 kO 18 kO
Figure p].66
7.67 The di fferential equat ion that describes the current io( l ) in a network is
d' io(t) di,,{l ) --,- + 6-- + 4io( l ) = 0 dr dt
Find (a) the characteristi c equation of the network, (b) the network 's natural frequencies, and (c) the expression fori,,(I).
7.68 The terminal current in a network is described by the equation
,I'io(l ) di, (I) --,- + 8- - + 16i,,{ l) = 0
dr dl
Find (a) the characteristi c equation of the network, (b) the network's natura l frequencies, and (c) the equati on for i,,{I ).
7.69 The voltage 'V I( t) in a network is defined by the equation
d'v,(l ) dv,(t) - -,- + 4-- + 5v,(t) = 0
dr dr
Find (a) the characteristic equation of the network, (b) the circuit's natural frequencies, and (c) the expression for v ,(t) .
7.70 The output voltage of a circuit is described by the differ-ential equation
d'vo ( I) dvo( I) --, - + 8-- + 10v.,{ l ) = 0
dt ' dt
Find (a) the characteristic equation of the circuit, (b) the network's natural frequencies, and (c) the equation for V,,(I).
C 771 The voltage vl{ t) in a network is defined by the equulion d'1) ,(I ) [ dV,(I)] --,- + 2 - - + 5v,(1) = 0 dl - dl
Find (a) the characteristic equation of the network. (b) the circu it's natural frequencies. (el the expression for V,( I).
2kO
C
0 +
7 kO Vo( I)
0
7.72 The parameters for a parallel RLC circuit are R = I n , L = 1/ 2 H. and C = 1/ 2 F. Determine the type of damping exhibited by the circuit.
7.73 A series RLC circui t contains a res istor of R = 2 nand 0 a capacitor C = 1/ 2 F. Select the value of the induclOr so that the circuit is critically damped.
7.74 A parallel RLC circuit contains a resistor I? = I nand 0 an inductor L = 2H. Se lect the value of the capacitor so that the circui t is critically damped.
7.75 For the underdamped circuit shown in Fig. P7.75, 0 determine the voltage v( t) if the initial conditions on the storage clements arc iJO) I A and v,(O) = 10 V.
2H
I Figure P].75
+ +
V(t) 50 1 ,~ vc(O) 40 F
7.76 In the criticall y damped circuit shown in Fig. P7.76. the 0 initial conditions on the storage clements ure i,.(O) = 2 A and v,(O) = 5 V. Determine the voltage v( t ).
+ +
vc(o) 'r 001 F v(t) 100 r
Figure P7.76 7.77 Find v,.{t) for t > 0 in the circuit in Fig. P7 .77 . ()
t = 0
+
1 A 80 0.04 F
Figure P7.77
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CHAP TE R 7 F IRS T - A N D SECON D - ORDE R TR ANS IEN T CI R CU IT S
() 7.78 Find V,(I) for I > 0 in the circuit in Fig. P7.78 if v,.(O) = O.
7.80 Find V,,(/) for I > 0 in the circuit in Fig. P7.80 and plot the response including the time interval just prior to moving the switch.
I ~ 0 1 k!l 100mH 2 k!l 1 mH
+
1 ~F vdl) + 12V 1 k!l Vo(l)
Figure P7.78 Figure P7.80
Find 'Vo(l ) for I > 0 in the circuit in Fig. P7.79 and plot the response including the time interval just prior to clos-ing the switch.
7.81 In the circuit shown in Fig. P7.8 1, fi nd V( I ) > O.
12V +
Figure P7.79
+
1 H 10!l 'Vo(l) Figure P7.81
~ H 5
20
7.82 Find ve(r) for I > 0 in the circui t in Fig. P7.82 and plot the response including the time interv'll just prior to moving the switch.
I ~ 0 1 mH
+
4 kO 1 k!l Vo(l)
Figure P7.82
7.83 Find V,,( / ) for I > 0 in the network in Fig. P7.83 and plot the response including the time interval just prior to moving the switch.
10 k!l Sk!l I ~ 0
100 V 10 k!l 2 kO
100 mH
Figure P7.83
1 T2 F
+
V(I)
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PROBLEMS 369
0 7.84 Find vQ(t) for [ > 0 in the circuit in Fig. P7.S4 and plOi the response includi ng the lime interval j ust prior to closing the switch.
1.5 A 40
Figure P7.84
80
so
~ H 8
o 7.8 5 The switch in the circui t in Fig. P7.85 has been closed D for a lo ng time and is opened at I = O. Find ;(1) for Ji:! / > o.
/ ~ 0
50 50
50
i(/) + 20 V 0.04 F
1 H
10 V
Figure p].8S
e 7.86 The switch in (ile c ircuit in Fig P7.86 has been closed for a long time and is opened at I = O. Find ;(t ) for / > o.
so
12V +
i(/)
1.25 H
Figure P7.86
1.50
/ ~ 0
0.1 F
SV
/ ~ 0 o I
.lH 8
+
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370 CHAPTER 7 FIRST AND SECOND ORDER TRANSIENT C I RC UITS
~ 7.87 Find V,,(I) fo r I > 0 in the circuit in Fig. P7.87 and plot the response including the time interval just prior to mov ing the switch.
7.88 Design a para lle l IILe eircllil with II ~ I ki1 0 that h
-
,/
7.92 Given the network in Fig. P7.92. use PSPICE to plot 'V"(I) over a 10-s interval starting al T = 0 using a IOO-nls step size .
. \ 2n -1~ 0 4n J
2H
12 V + 6n 2A t ,,'" - + 1 F 2n vo(t)
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figure P7.92 7.93 Given the network in Fig. P7.93. use PSPICE to plot V"(I ) over a 10-s
interval starting at t :::: 0 usi ng a IOO-ms step size.
1 ~ 0 12 V 20 kn 10 kn
6V + ---{) 50 ",F +
10mH 5 kn Vo(t)
figure P7.93
7.94 Given (he network in Fig. P7.94a and the input voltage shown in Fig. P7.94b, use PSPICE to plot the voltage V(,( t ) over the interval 0 :5 ( :s 4 s using a 20-ms step size.
100 kn 1Mn +
Vil1(t) 2mH 0.1 ",F Vo(t)
0
(a) Vil1(t) V
10
o 1 (5) (b)
figure P7.94
PROBLEMS 371
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372 CHAPTER 7 FIRST - AND SECOND-ORDER TRANSIENT CIRCU I TS
7.95 Given the network in Fig. P7.95a, and the input voltage shown in Fig. P7.95b, plot 'V1I(t) using PSPICE over the interval 0 :::s: ( :::s: 10 s using a IOO-ms-slep size.
+
Vin(r) 20 20 20 +
1 F ;o p;: ~2A ! 1 H 1 0 40 Vo t -
0
(al
10
o r (s) (bl
Figure P7.95
7.96 Given the network in Fig. P7.96a and the input in Fig. P 7.96b, lise PSPICE to plot vo( r) in the interval 0 :::::: r :5 4 5 using a 20-ms step size.
10 kO
1/
5 kO 100'~F + v,(r) r 10 mH ! 10 kO vo(r)
(al v,(r) V
10 r-- .--
o 2 3 4 r (s) (bl
Figure P7.96
(r)
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T YP I CAL PR O B LE MS F OUND ON THE FE E XAM 373
TYPICAL PROBLEMS FOUND ON THE FE EXAM
7FE-1 In the circu it in Fig. 7PFE- I. the switch, which has been closed for a long time. opens at [ = O. Find the value of the capacitor voltage V,(I) a ll ~ 2s. a. 0.936 V b. 0.756 V c. 0.264 V d. 0.462 V
I ~ a 8 kO 6 kO
+
12 V 6 kO vc(t) 100 ~F 6 kO
Figure 7PFE-l
7FE-2 In the network in Fig. 7PFE2. the switch closes all = O. Find vo( t ) at I = Is. a. 5.62 V b. 1.57 V c . 4.25 V d. 3.79 V
12 kO 4kO
12 V 12 kO
~-----~O I ~ O __ _ _ ~ +
100 ~F vo(t)
Figure 7PFE-2 7FE-3 Assume that the switch in the network Fig. 7PFE-3 has been closed for
some time. At [ = 0 the switch opens. Determine the time required for the capacitor voltage to decay 10 one-half of its initially charged value. a. 0.4 16 s b. 0.6255 c. 0.235 s d. 0.143 s
12 kO
+
12V Vc( I) 100 ~F 6kO
Figure 7PFE-3
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374 CHAP T E R 7 FI RST, AND SECONDORDER TRA N S I E NT C I RC U ITS
7FE ~4 Find the inductor current it( r) for r > 0 in the circui t in Fig. 7PFE-4. a. i 1.( I) = 3 - 2e- ,/6 A, 1 > a h. i,.(r ) = I + 2e- 21 / 3 A, r > 0 c. i,.(I) = 6 - e-'/6 A, 1 > a d. i 1.( I ) = 3 - e-2,/.\ A, I > a
t = 0 20
10 V 2 0 20 1 A
Figure 7PFE'4
7FES Find the inductor current il.(I) for 1 > a in the circuit in Fig. 7PFE5.
a. i1.( I) = 1.4 + 0.4e- " iJ A , 1 > 0 b. i 1.( I ) = 1.2 + 0.4e- " i3 A , 1 > 0 c. i,.( I) = 0.4 + 0.2e-" /3 A, 1 > 0 d. il,(I) = 2.4 + 0.6e- ', /3 A, 1 > 0
30
12V + 40 40
Figure 7PFE'5
