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CYU 41 Plot for Check Your Understanding 41
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0 002 004 Inductor voltage for Exercise 41
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006 008 01 012 014 0 2 4 t (s) 6 8 10
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Part I
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Circuits
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CYU 42
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Capacitor current for Exercise 42
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iC (t) (mA)
3 2 1 0 0 2 4 t (s) 6 8 10
CYU 43 CYU 44 CYU 45
w(t = 3 ms) = 39 J w(t = 3 ms) = 2222 mJ 6 5625 10 J 0156 10 6 t 2 25 10 6 t w(t) = +10 5 0625 10 6 p(t) = 0 t < 2 ms 2 t < 6 ms t 6 ms 2 t < 6 ms otherwise
(20 10 3 25t) ( 0125) W 0
CYU 46 CYU 47 CYU 48 CYU 49 CYU 410 CYU 413
v(t) = 1556 cos(377t ) 6 v(t) = 25 V v(t) = 15 V 289 V 05 V V 1 + ( RC)2
= tan 1 ( RC) CYU 414 CYU 415 CYU 416 CYU 417 CYU 418 CYU 419 CYU 420 CYU 421 (a) v1 + v2 = 467 cos( t + 03526 ); (b) v1 + v2 = 608 cos( t 06562 ) (a) i1 + i2 = 019 cos( t + 0733 ); (b) i1 + i2 = 132 cos( t 05637 ) Z(1,000) = 140 j 10; Z(100,000) = 100 + j 999 YEQ = 5492 10 3 j 4871 10 3 X = 025; C = 04 F |IS | = 00041 A; 00083 A; 00194 A; 002 A; 002 A 7424e j 0381 22ej 0 A
4
AC Network Analysis
HOMEWORK PROBLEMS
Section 1: Energy Storage Elements 41 The current through a 05-H inductor is given by
iL = 2 cos(377t + /6) Write the expression for the voltage across the inductor
46 Find the energy stored in each capacitor and
inductor, under steady-state conditions, in the circuit shown in Figure P46
42 The voltage across a 100- F capacitor takes the
following values Calculate the expression for the current through the capacitor in each case a vC (t) = 40 cos(20t /2) V b vC (t) = 20 sin 100t V c vC (t) = 60 sin(80t + /6) V d vC (t) = 30 cos(100t + /4) V
2H 3F
43 The current through a 250-mH inductor takes the
following values Calculate the expression for the voltage across the inductor in each case a iL (t) = 5 sin 25t A b iL (t) = 10 cos 50t A c iL (t) = 25 cos(100t + /3) A d iL (t) = 20 sin(10t /12) A
Figure P46
47 Find the energy stored in each capacitor and
inductor, under steady-state conditions, in the circuit shown in Figure P47
44 In the circuit shown in Figure P44, let
i(t) = 0 =t = (t 2) =0 for < t < 0 for 0 t < 1 s for 1 s t < 2 s for 2 s t <
1 1H
2H 1F 12 V 6
i(t)
Figure P47
48 The plot of time-dependent voltage is shown in
Figure P44
Find the energy stored in the inductor for all time
Figure P48 The waveform is piecewise continuous If this is the voltage across a capacitor and C = 80 F, determine the current through the capacitor How can current ow through a capacitor
v(t) (V) 20 10 5 10 10 15 t (ms)
45 In the circuit shown in Figure P45, let
v(t) = 0 = 2t = (2t 4) =0 for < t < 0 for 0 t < 1 s for 1 s t < 2 s for 2 s t <
v(t)
01 F
Figure P48
Figure P45
49 The plot of a time-dependent voltage is shown in
Figure P48 The waveform is piecewise continuous If this is the voltage across an inductor L = 35 mH,
Find the energy stored in the capacitor for all time
Part I
Circuits
determine the current through the inductor Assume the initial current is iL (0) = 0
410 The voltage across an inductor plotted as a function
of time is shown in Figure P410 If L = 075 mH, determine the current through the inductor at t = 15 s
v(t) (V) 35 5 19 10 15 t ( s)
a Resistor R = 7 b Capacitor C = 05 F c Inductor L = 7 mH
v(t) (V) 15 10 5 5 10 t (ms)
Figure P413 Figure P410
414 If the plots shown in Figure P414 are the voltage 411 If the waveform shown in Figure P411 is the
voltage across a capacitor plotted as a function of time with: vPK = 20 V T = 40 s C = 680 nF across and the current through an ideal capacitor, determine the capacitance
v(t) (V) 10 5 10 10 5 s vPK T 2T t 12 i(t) (A) 12 5 10 15 t (ms) 15 t (ms)
determine and plot the waveform for the current through the capacitor as a function of time
Figure P411
412 If the current through a 16 h inductor is zero at
t = 0 and the voltage across the inductor (shown in Figure P412) is: vL (f ) = 0 = 3t 2 = 12 nV t <0 0 < t < 20 s
Figure P414
415 If the plots shown in Figure P415 are the voltage
across and the current through an ideal inductor, determine the inductance
v(t) (V)
t > 20 s
2 1 5 10 15 t (ms)
determine the current through the inductor at t = 30 s
v(t) (nV ) 12 20 40 t ( s)
i(t) (V) 3 2
Figure P412
1 5 10 15 t (ms)
413 Determine and plot as a function of time the
current through a component if the voltage across it has the waveform shown in Figure P413 and the component is a:
Figure P415
4
AC Network Analysis
416 The voltage across and the current through a
capacitor are shown in Figure 416 Determine the value of the capacitance
v(t) (v)
1 v(t) (V) 15 10 5 5 10 t (ms) ic(t) (mA) 15 5 10 t (ms) 0 9 2 4 6
t (ms)
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