d What are the maximum amplitude, frequency in radians per second, and phase angle of the steady-state current.. 9.12 The expressions for the steady-state voltage and current at the ter
Trang 1346 Sinusoidal Steady-State Analysis
in Fig 9.57 depicts these observations The dotted
phasors represent the pertinent currents and
volt-ages before the addition of the capacitor
Thus, comparing the dotted phasors of I, RJL,
ja>L-[l, and Vv with their solid counterparts clearly
shows the effect of adding C to the circuit In
par-ticular, note that this reduces the amplitude of the
source voltage and still maintains the amplitude of
the load voltage Practically, this result means that,
as the load increases (i.e., as Ia and Ih increase), we
can add capacitors to the system (i.e., increase Ic)
so that under heavy load conditions we can
main-tain VL without increasing the amplitude of the
source voltage
Figure 9.56 • The effect of the capacitor current Ic on the line current I
Figure 9.55 • The addition of a capacitor to the circuit shown
in Fig 9.53
Figure 9.57 A The effect of adding a load-shunting capacitor to the circuit shown in Fig 9.53 if VL is held constant
NOTE: Assess your understanding of this material by trying Chapter Problems 9.84 and 9.85
Practical Perspective
A Household Distribution Circuit
Let us return to the household distribution circuit introduced at the begin-ning of the chapter We will modify the circuit slightly by adding resistance
to each conductor on the secondary side of the transformer to simulate more accurately the residential wiring conductors The modified circuit is shown
in Fig 9.58 In Problem 9.88 you will calculate the six branch currents on the secondary side of the distribution transformer and then show how to calculate the current in the primary winding
NOTE: Assess your understanding of this Practical Perspective by trying Chapter Problems 9.88 and 9.89
— h
13.2/0!
kV
• +
1(1
-AAA-• +
120/0! l | 2 0 O
AW
[3
-.— r,
120/0! j i40 0
-VW *
10 nf iii
Figure 9.58 • Distribution circuit
Trang 2Summary
The general equation for a sinusoidal source is
v = V m cos(a)t + 4>) (voltage source),
or
i = I m cos(a»r + (j>) (current source),
where V m (or I m ) is the maximum amplitude, a> is the
frequency, and <f) is the phase angle (See page 308.)
The frequency, a>, of a sinusoidal response is the same as
the frequency of the sinusoidal source driving the circuit
The amplitude and phase angle of the response are
usu-ally different from those of the source (See page 311.)
The best way to find the steady-state voltages and
cur-rents in a circuit driven by sinusoidal sources is to
per-form the analysis in the frequency domain The following
mathematical transforms allow us to move between the
time and frequency domains
• The phasor transform (from the time domain to the
frequency domain):
V = V m e^ = &{V m cos(tot + <£)}
• The inverse phasor transform (from the frequency
domain to the time domain):
(See pages 312-313.)
When working with sinusoidally varying signals,
remember that voltage leads current by 90° at the
ter-minals of an inductor, and current leads voltage by 90°
at the terminals of a capacitor (See pages 317-320.)
Impedance (Z) plays the same role in the frequency
domain as resistance, inductance, and capacitance play
in the time domain Specifically, the relationship
between phasor current and phasor voltage for
resis-tors, inducresis-tors, and capacitors is
V = 2 1 ,
where the reference direction for I obeys the passive sign convention The reciprocal of impedance is
admittance (Y), so another way to express the
current-voltage relationship for resistors, inductors, and capaci-tors in the frequency domain is
v = i/y
(See pages 320 and 324.)
All of the circuit analysis techniques developed in Chapters 2-4 for resistive circuits also apply to sinu-soidal steady-state circuits in the frequency domain These techniques include KVL, KCL, series, and paral-lel combinations of impedances, voltage and current division, node voltage and mesh current methods, source transformations and Thevenin and Norton equivalents
The two-winding linear transformer is a coupling device
made up of two coils wound on the same nonmagnetic
core Reflected impedance is the impedance of the
sec-ondary circuit as seen from the terminals of the primary circuit or vice versa The reflected impedance of a linear transformer seen from the primary side is the conjugate
of the self-impedance of the secondary circuit scaled by
the factor (a)M/\Z 22 \) 2 (See pages 335 and 336.)
The two-winding ideal transformer is a linear
trans-former with the following special properties: perfect
coupling (k = 1), infinite self-inductance in each coil
(Z-! = L2 = oo), and lossless coils (R { = R 2 = 0) The circuit behavior is governed by the turns ratio a = N 2 /N]_
In particular, the volts per turn is the same for each winding, or
Afc*
and the ampere turns are the same for each winding, or
JVili = ± N 2 l 2
-(See page 338.)
TABLE 9.3 Impedance and Related Values
Element Impedance (Z)
Resistor R (resistance)
Capacitor ;(—l/a»C)
Inductor jwL
Reactance
- 1/wC
coL
Admittance (Y)
G (conductance) j(oC
}{-\/a>L)
Susceptance
-1/coL
Trang 3348 Sinusoidal Steady-State Analysis
Problems
Section 9.1
9.1 Consider the sinusoidal voltage
v(t) = 80 cos (lOOOirt - 30°) V
a) What is the maximum amplitude of the voltage?
b) What is the frequency in hertz?
c) What is the frequency in radians per second?
d) What is the phase angle in radians?
e) What is the phase angle in degrees?
f) What is the period in milliseconds?
g) What is the first time after t = 0 that v = 80 V?
h) The sinusoidal function is shifted 2/3 ms to the
left along the time axis What is the expression
for v(t)l
i) What is the minimum number of milliseconds
that the function must be shifted to the right if
the expression for v(t) is 80 sin 100()7r/ V?
j) What is the minimum number of milliseconds
that the function must be shifted to the left if the
expression for v(t) is 80 cos IOOO77-? V?
9.2 At t = — 2 ms, a sinusoidal voltage is known to be
zero and going positive The voltage is next zero at
t = 8 ms It is also known that the voltage is 80.9 V
at t = 0
a) What is the frequency of v in hertz?
b) What is the expression for vl
9.3 A sinusoidal current is zero at t = — 625/xs and
increasing at a rate of 800077 A/s The maximum
amplitude of the current is 20 A
a) What is the frequency of i in radians per second?
b) What is the expression for /?
9.4 A sinusoidal voltage is given by the expression
v = 10 cos (3769.911 - 53.13°) V
Find (a) / in hertz; (b) T in milliseconds; (c) V m ;
(d) v(0); (e) <£ in degrees and radians; (f) the smallest
positive value of t at which v = 0; and (g) the
small-est positive value of t at which dv/dt = 0
9.5 In a single graph, sketch v = 100 cos (cot + 4>)
ver-sus cot for 4> = - 6 0 ° , - 3 0 ° , 0°, 30°, and 60°
a) State whether the voltage function is shifting to
the right or left as <f> becomes more positive
b) What is the direction of shift if 4> changes from
0 t o 3 0 ° ?
9.6 Show that
/ '
9.7 The rms value of the sinusoidal voltage supplied to the convenience outlet of a home in Scotland is
240 V What is the maximum value of the voltage
at the outlet?
9.8 Find the rms value of the half-wave rectified sinu-soidal voltage shown
Figure P9.8
K„,sin^r£,0 t« 7/2
37/2
Section 9.2
Vj, cos2(wr -I- (j>)dt = VlT
9.9 The voltage applied to the circuit shown in Fig 9.5
at t = 0 is 20 cos (800* + 25°) V The circuit
resist-ance is 80 fl and the initial current in the 75 mH inductor is zero
a) Find i(t) for t > 0
b) Write the expressions for the transient and
steady-state components of i(t)
c) Find the numerical value of i after the switch has
been closed for 1.875 ms
d) What are the maximum amplitude, frequency (in radians per second), and phase angle of the steady-state current?
e) By how many degrees are the voltage and the steady-state current out of phase?
9.10 a) Verify that Eq 9.9 is the solution of Eq 9.8 This
can be done by substituting Eq 9.9 into the left-hand side of Eq 9.8 and then noting that it
equals the right-hand side for all values of t > 0
At t = 0, Eq 9.9 should reduce to the initial
value of the current
b) Because the transient component vanishes as time elapses and because our solution must sat-isfy the differential equation for all values of /, the steady-state component, by itself, must also satisfy the differential equation Verify this observation by showing that the steady-state component of Eq 9.9 satisfies Eq 9.8
Sections 9.3-9.4 9.11 Use the concept of the phasor to combine the
fol-lowing sinusoidal functions into a single trigono-metric expression:
a) y = 50 cos(500/ + 60°) + 100 cos(500* - 30°), b) y = 200 cos(377/ + 50°) - 100 sin(377/ + 150°),
Trang 4c) y = 80 cos(100f + 30°) - 100 sin(100f - 135°)
+ 50 cos(100r - 90°), and
d) v = 250 cos oit + 250 cos(wr + 120°)
+ 250 cos(o* - 120°)
9.12 The expressions for the steady-state voltage and
current at the terminals of the circuit seen in
Fig P9.12 are
v g = 300 cos ( 5 0 0 0 ^ + 78°) V,
i g = 6sin(50007rf + 123°) A
a) What is the impedance seen by the source?
b) By how many microseconds is the current out of
phase with the voltage?
Figure P9.12
9.13 A 80 kHz sinusoidal voltage has zero phase angle
and a maximum amplitude of 25 mV When this
voltage is applied across the terminals of a
capaci-tor, the resulting steady-state current has a
maxi-mum amplitude of 628.32 /xA
a) What is the frequency of the current in radians
per second?
b) What is the phase angle of the current?
c) What is the capacitive reactance of the capacitor?
d) What is the capacitance of the capacitor in
microfarads?
e) What is the impedance of the capacitor?
9.14 A 400 Hz sinusoidal voltage with a maximum
amplitude of 100 V at t = 0 is applied across the
terminals of an inductor The maximum amplitude
of the steady-state current in the inductor is 20 A
a) What is the frequency of the inductor current?
b) If the phase angle of the voltage is zero, what is
the phase angle of the current?
c) What is the inductive reactance of the inductor?
d) What is the inductance of the inductor in
millihenrys?
e) What is the impedance of the inductor?
Sections 9.5 and 9.6
9.15 A 40 H resistor, a 5 mH inductor, and a 1.25/xF
PSPICE capacitor are connected in series The series-connected
elements are energized by a sinusoidal voltage source whose voltage is 600 cos (8000^ + 20°)V
a) Draw the frequency-domain equivalent circuit b) Reference the current in the direction of the voltage rise across the source, and find the pha-sor current
c) Find the steady-state expression for i(t)
9.16 A 10 O resistor and a 5 /xF capacitor are connected
PSPICE in parallel This parallel combination is also in
par-1 allel with the series combination of an 8 O resistor and a 300 /xH inductor These three parallel branches are driven by a sinusoidal current source whose current is 922 cos(20,000r + 30°) A
a) Draw the frequency-domain equivalent circuit b) Reference the voltage across the current source
as a rise in the direction of the source current, and find the phasor voltage
c) Find the steady-state expression for v{t)
9.17 a) Show that, at a given frequency w, the circuits in
Fig P9.17(a) and (b) will have the same imped-ance between the terminals a,b if
2 J 2
/e, - a> z LjR 2
R\ + co 2 L 22
R\ + (o 2 L\
b) Find the values of resistance and inductance that when connected in series will have the same impedance at 4 krad/s as that of a 5 kH resistor connected in parallel with a 1.25 H inductor
Figure P9.17 'a
Ri \U
L,
9.18 a) Show that at a given frequency eo, the circuits in
Fig P9.17(a) and (b) will have the same imped-ance between the terminals a,b if
Ro = R] + a?L\
u = R\ + o)2 f 2 L\
(Hint: The two circuits will have the same
impedance if they have the same admittance.) b) Find the values of resistance and inductance that when connected in parallel will have the same impedance at 1 krad/s as an 8 kft resistor con-nected in series with a 4 H inductor
Trang 5350 Sinusoidal Steady-State Analysis
9.19 a) Show that at a given frequency to, the circuits in
Fig P9.19(a) and (b) will have the same
imped-ance between the terminals a,b if
/?i =
Q =
R 2
1 + o?R\c\
1 + arRJCJ
w 2 RJC 2
b) Find the values of resistance and capacitance
that when connected in series will have the same
impedance at 40 krad/s as that of a 1000 ft
resis-tor connected in parallel with a 50 nF capaciresis-tor
Figure P9.19
'a
A',
c,;
c,
(a)
9.20 a) Show that at a given frequency QJ, the circuits in
Fig 9.19(a) and (b) will have the same
imped-ance between the terminals a,b if
R 2
C\
1 + (D 2 R]C\
orR { C 2
1 + io 2 R]C\
(Hint: The two circuits will have the same
impedance if they have the same admittance.)
b) Find the values of resistance and capacitance that
when connected in parallel will give the same
impedance at 50 krad/s as that of a 1 kft resistor
connected in series with a capacitance of 40 nF
9.21 a) Using component values from Appendix H,
combine at least one resistor, inductor, and
capacitor in series to create an impedance of
300 - /400 ft at a frequency of 10,000 rad/s
b) At what frequency does the circuit from part (a)
have an impedance that is purely resistive?
9.22 a) Using component values from Appendix H,
combine at least one resistor and one inductor
in parallel to create an impedance of
40 + /20 ft at a frequency of 5000 rad/s
(Hint-Use the results of Problem 9.18.)
b) Using component values from Appendix H, combine at least one resistor and one capacitor
in parallel to create an impedance of
40 - /20 ft at a frequency of 5000 rad/s (Hint:
Use the result of Problem 9.20.) 9.23 a) Using component values from Appendix H, find
a single capacitor or a network of capacitors
that, when combined in parallel with the RL
cir-cuit from Problem 9.22(a), gives an equivalent impedance that is purely resistive at a frequency
of 5000 rad/s
b) Using component values from Appendix H, find
a single inductor or a network of inductors that,
when combined in parallel with the RC circuit
from Problem 9.22(b), gives an equivalent impedance that is purely resistive at a frequency
of 5000 rad/s
9.24 Three branches having impedances of 3 + /4 O,
16 - /12 ft, and - / 4 ft, respectively, are connected
in parallel What are the equivalent (a) admittance, (b) conductance, and (c) susceptance of the parallel connection in millisiemens? (d) If the parallel branches are excited from a sinusoidal current
source where i = 8 cos w/ A, what is the maximum
amplitude of the current in the purely capacitive branch?
9.25 a) For the circuit shown in Fig P9.25, find the
fre-PSPICE quency (in radians per second) at which the
impedance Za b is purely resistive, b) Find the value of Za b at the frequency of (a)
Figure P9.25
160/tH
a « TVYV^
25 nF
9.26 Find the admittance K,b in the circuit seen in Fig P9.26 Express K(lb in both polar and
rectangu-lar form Give the value of Y ab in millisiemens
Figure P9.26 -/12.8 ft a*
>V
6 ft -{/12 ft
5 f t |/10 ft
13.6 ft
Trang 69.27 Find the impedance Za b in the circuit seen in 9.31 Find the steady-state expression for /„(/) in the
cir-Fig P9.27 Express Za b in both polar and rectangular PSPICE c ui t in Fig P9.31 if v s = 100 sin 50/ mV
Figure P9.27
1 Q a«
'vw-Zau
-/8 n
40 n
:10O
^ -/20 n
!/20 0
Figure P9.31
412 240 mH
VW o r w x
2.5 mF
9.32 Find the steady-state expression for v (> in the circuit
of Fig P9.32 if i g = 500 cos 2000/ m A
9.28 The circuit shown in Fig P9.28 is operating in the
sinusoidal steady state Find the value of co if
i (} = 40 sin (a)/ + 21.87°) mA
v g = 40cos(o>/ - 15°) V
Figure P9.28
600 tt 3.2 H
^ Y Y Y V
2.5 /xF
9.29 The circuit in Fig P9.29 is operating in the
sinu-PSPICE soidal steady state Find the steady-state expression
M"LTISIM fo r V w(f)i f u = 40 cos 50,000/ V
Figure P9.29
1/u.F
Figure P9.32
<0
120 a
12.5/tF
40 a +
60 mH iv
9.33 The phasor current Ia in the circuit shown in
PSPICE Fig P9.33 is 2 / 0 ° A lumsiM
a) Find Ib, Ic, and Vg
b) If a) = 800 rad/s, write the expressions for i b (t),
/c(/), and vM)
Figure P9.33
120 n
"4
/ 4 0 a
-6 +/3.5 AI ©
9.30 a) For the circuit shown in Fig P9.30, find the
steady-PSPICE state expression for v () if /„ = 2 cos (16 X 10^/) A
MULTISIM
b) By how many nanoseconds does v a lag /',,?
Figure P9.30
9.34 The circuit in Fig P9.34 is operating in the sinusoidal
PSPICE steady state Find v 0 (t) if /,(/) = 3 cos 200/ mA
MULTISIM
Figure P9.34
6ft
r^
.©J : 22 n ^ "12.5mFj2mH : :5 n
+
vjt)
•
Trang 7352 Sinusoidal Steady-State Analysis
9.35 Find the value of Z in the circuit seen in Fig P9.35
if V g = 100 - /50 V, Ig = 30 + /20 A, and
\i = 140 + /30 V
Figure P9.35
7,
20 a 12 a /16 a
-A/W
/5 ft Vj
9.39 The frequency of the sinusoidal voltage source in
PSPICE the circuit in Fig P9.39 is adjusted until the current
"1ULTISIM • • • i ; « _
i a is in phase with v g
a) Find the frequency in hertz
b) Find the steady-state expression for i g (at the
frequency found in [a]) if v g = 30 cos wt V
9.36 Find Ib and Z in the circuit shown in Fig P9.36 if
VJJ = 2 5 / ( T V and Ia = 5 / 9 0 ° A
Figure P9.36
••©
!/3 a
i n
- / 2 ft
-/5 n
4n
K
^ -/3 n
9.37 Find Za b for the circuit shown in Fig P9.37
Figure P9.37
PSPICE MULTISIM
- / i n
9.38 a) The frequency of the source voltage in the circuit
in Fig P9.38 is adjusted until i g is in phase with
V r What is the value of co in radians per second?
b) If v g = 20 cos a)t V (where a> is the frequency
found in [a]), what is the steady-state expression
for v n l
PSPICE
MULTISIM
Figure P9.38
500 n {1?
\ 500 mH v„ 1 1 kn
Figure P9.39
(50/3) k i l 1.2 kn
>vw-200 mH
9.40 The circuit shown in Fig P9.40 is operating in the
PSPICE sinusoidal steady state The capacitor is adjusted
' until the current L is in phase with the sinusoidal voltage Vg-
a) Specify the capacitance in microfarads if
Vg = 80 cos 5000f V
b) Give the steady-state expression for L when C
has the value found in (a)
Figure P9.40
800 mH
9.41 a) The source voltage in the circuit in Fig P9.41 is
Vg - 50 cos 50,000f V Find the values of L such that ig is in phase with v g when the circuit is operating in the steady state
b) For the values of L found in (a), find the steady-state expressions for ig
Figure P9.41
5nF
10 kn
9.42 The frequency of the sinusoidal current source in
PSPICE the circuit in Fig P9.42 is adjusted until v a is in mTISIM phase with i r
a) What is the value of a) in radians per second? b) If ig = 2.5 cos oit mA (where to is the frequency
found in [a]), what is the steady-state expression for u,?
Trang 8Figure P9.42
50 nF
Section 9.7
9.43 T h e device in Fig P9.43 is r e p r e s e n t e d in the
fre-quency domain by a N o r t o n equivalent W h e n a
resistor having an impedance of 5 k f t is connected
across t h e device, the value of V 0 is 5 — /15 V
When a capacitor having an impedance of - / 3 kft
is connected across the device, the value of I () is
4.5 - / 6 m A Find the N o r t o n current I N and the
N o r t o n i m p e d a n c e Z N
Figure P9.43
I A f +
Device
9.44 The sinusoidal voltage source in the circuit
in Fig P9.44 is developing a voltage equal t o
247.49 cos (lOOOf+ 45°) V
a) Find the Thevenin voltage with respect to the
terminals a,b
b) Find the Thevenin impedance with respect t o
the terminals a,b
c) D r a w the Thevenin equivalent
Figure P9.44
< D
100 mH
iioon
JlOOmH
(
^ 1 0 A i F
» o b
9.45 U s e source transformations t o find the Thevenin
equivalent circuit with respect to t h e terminals a,b
for the circuit shown in Fig P9.45
Figure P9.45
240/0° V
/60 ft
36 a
9.46 U s e source transformations t o find the N o r t o n
equivalent circuit with respect t o the terminals a,b for the circuit shown in Fie P9.46
Figure P9.46
/60 ft
30 ft
- A M / *
-/100 ft
9.47 Find the Thevenin equivalent circuit with respect to
the terminals a,b for the circuit shown in Fig P9.47 Figure P9.47
/4 0
4 ft:
4 ft:
l f t
• A A A
-60/0° V
x
4ft
4ft -/4 ft
- • b
9.48 Find t h e Thevenin equivalent circuit with respect to
the terminals a,b of t h e circuit shown in Fig P9.48
Figure P9.48
2504)° V
20 ft /10 ft
9.49 Find the N o r t o n equivalent with respect to
termi-nals a,b in the circuit of Fig P9.49
Figure P9.49
6½
1 ( ) / - 4 5 ° A ( f ) 2 f t | / l f t
IK
9.50 Find Za b in the circuit shown in Fig P9.50 when the circuit is operating at a frequency of 100 k r a d / s
Figure P9.50
Trang 9354 Sinusoidal Steady-State Analysis
9.51 Find the Thevenin impedance seen looking into the
terminals a,b of the circuit in Fig P9.51 if the
fre-quency of operation is (25/TT) kHz
Figure P9.51
2.5 nF
am— 2.4 kfl
>s
39/A 5nF
:9on
:3.3 kO
9.52 Find the Norton equivalent circuit with respect to
the terminals a,b for the circuit shown in Fig P9.52
whenVy = 5 / 0 ° V
9.53 The circuit shown in Fig P9.53 is operating at a
fre-quency of 10 rad/s Assume a is real and lies
between - 1 0 and +10, that is, - 1 0 < a < 10
a) Find the value of a so that the Thevenin
imped-ance looking into the terminals a,b is purely
resistive
b) What is the value of the Thevenin impedance for
the a found in (a)?
c) Can a be adjusted so that the Thevenin
impedance equals 500 — /500 O? If so, what is
the value of a ?
d) For what values of a will the Thevenin
imped-ance be inductive?
Figure P9.53
100/uF
a«-»A S1 kfl '«%
Section 9.8
9.54 Use the node-voltage method to find the
steady-PSPICE state expression for v() (t) in the circuit in Fig P9.54 if
MULTISIM
% = 20cos(2000r - 36.87°) V,
Figure P9.54
1 mH
9.55 Use the node-voltage method to find \ (> in the
cir-cuit in Fig P9.55
Figure P9.55
240/0° V
/ion /io a
50 n
+
v., 30 il
9.56 Use the node-voltage method to find the phasor
voltage V« in the circuit shown in Fig P9.56
Figure P9.56
-/4 n
-/812 + V„
1211
9.57 Use the node voltage method to find the steady-state
PSPICE expressions for the branch currents /a, ib, and /c in the
MULTISIM circuit seen in Fig P9.57 if v& = 50sinl0fVV and
V b = 25 cos (106/ + 90°) V
Figure P9.57
i ?"»
100 nF 1/
K
lOfxH
i
lion
i
IO a
1 ^v b
v = 50sin(2000r - 16.26°) V
Trang 109.58 U s e t h e node-voltage m e t h o d to find Vf) a n d I„ in t h e
circuit seen in Fig P9.58
Figure P9.58
Figure P9.63
f )6+yl3 mA | 5 0 O (
9.59 U s e t h e node-voltage m e t h o d t o find t h e p h a s o r
voltage V„ in the circuit shown in Fig P9.59 Express
the voltage in b o t h polar a n d rectangular form
Figure P9.59
10+/10
Section 9.9
9.60 U s e t h e m e s h - c u r r e n t m e t h o d to find t h e
steady-state expression for v a (t) in t h e circuit in Fig P9.54
9.61 U s e t h e mesh-current m e t h o d to find t h e
steady-state expression for i () {t) in t h e circuit in Fig P9.61 if
v a = 60 cos 40,000/ V,
v h = 90 sin (40,000* + 180°) V
Figure P9.61
25 fiF
9.62 U s e the mesh-current m e t h o d t o find t h e phasor
current l g in t h e circuit in Fig P9.56
9.63 U s e t h e m e s h - c u r r e n t m e t h o d t o find t h e branch
currents I.„ Ih, Ic, a n d Id in t h e circuit shown in
Fig P9.63
i dJc A
5 a
9.64 U s e t h e mesh-current m e t h o d t o find t h e
steady-PSPICE st a t e expression for v a in t h e circuit seen in
« " » " Fig< p 9 64 if v e q u a|s \ 3 0 C Os 10,000/ V
Figure P9.64
5mH
*©
40 a
30iA
+
100 O 5 »„
Sections 9.5-9.9 9.65 U s e t h e concept of current division t o find t h e
PSPICE steady-state expression for i (> in t h e circuit in Mum™ pig P9.65 if/^ = 125 cos 12,500* m A
Figure P9.65
9.66 U s e t h e concept of voltage division t o find t h e
PSPICE steady-state expression for v () (t) in the circuit in
™LTISIM F i g p 9 6 6 i f v = 7 5 c o s 20,000/ V Figure P9.66
12 kO
— V A >
-3.125 nF