Example 1: (based on #26 Ch 10, Boylestad’s Circuit Analysis – 3rd Canadian Ed., CDROM)
For the circuit shown in the accompanying sketch:
a) Find the expressions for iC and vC for the period after
the switch is closed (note the initial charge on the
capacitor!)
vC(t) = = 100 -134e-212.8tV
b) Sketch the waveforms for iC and vC .
c) At what time(s) is vC = 0?
t = 1.38ms
Example 2: ((based on #29, Chapter 12, Boylestad’s Circuit Analysis – 3rd Can. Ed., CDROM)
[1]
The switch shown in the diagram has been closed for a
long time (>>5τ). Determine the maximum voltage that
will be observed across the terminals of the open switch
immediately after (t = 0+) it is opened.
Vsw = -51.27V
+ Vsw -
Example 3: (based on 2010 midterm)
For the following waveform,
determine the parameters listed
below.
200
V
170V
180
160
140
120
a) The phase offset, φ , in
degrees:
φ = -360
100
80
60
40
20
-0.01
-0.005
0
-20
-40
t (s)
0.005
0.01
0.015
0.02
t = 1.6667ms
-60
b) The peak-to-peak
voltage:
VP-P:340V
-80
-100
-100V
-120
-140
-160
-180
-200
c) The period. T:
T: ______________________
T = 16.67ms
d) The sinusoidal voltage v = 200 sin(2π1000t + 60°)V is plotted in (a) below;
determine the time t1. t1 = .333ms
e) The sinusoidal current i = 4 sin(50,000t - 40°)A is plotted in (b) below; determine
the time t1. t1 = 13.96µs
0.025
Example 4: (based on #5, Chapter 15, Boylestad’s Circuit Analysis – 2nd Canadian Ed.
CDROM)
Calculate the total impedance of the circuits below. Express your answer in rectangular
and polar forms, and draw the impedance diagrams showing each element and the total.
a) Z = (3 –j3)Ω = 4.24∠-450Ω
b) Z = (.5 +j3)kΩ = 3.04∠80.530 kΩ
c) Z = (47 +j1617.7)Ω = 1618.4∠88.30Ω
j
j
XL
XL
R
XL
j
Z
XL
Z
XL
R
R
XC
Z
XC
XC
(a)
(b)
Example 5: ( Based on Boylestad’s 3rd Can. Ed. Ch. 15, Q10)
For the circuit shown at right:
a) Find the total impedance, ZT in polar form.
ZT= 4.4472∠-63.435Ω
b) Find the value of C (in µF) and L (in H).
C = 265.25µF
XL = 15.915mH
(c)
c) Find the current, I, and the voltages across each element in phasor notation and give
the sinusoidal expression.
j
I = 11.18∠63.435A
VR = 22.36∠63.435V = 31.608sin(377t+63.435o)V
VL = 67.08∠153.435V = 94.865sin(377t +153.435o)V
VC = 111.8∠-26.565V = 158.109sin(377t -26.565o)V
IS
VL
VR
E
VC
Example 6: (Based on Boylestad’s 3rd Can. Ed. Ch. 19, Q5)
Consider the complex power loads
connected to a 240V source as shown in the
figure.
Determine:
a) The total real, reactive and apparent
power. Draw the power triangle.
b) Determine the source current, IS, and total impedance, ZT, seen by the source.
c) Find the power factor, FP, for the combined loads as shown.
d) Determine the type, value and VA rating of the reactive element needed to correct
the power factor to 1.
a)
Load
1
2
3
4
total
P(W)
300
1000
200
100
1600
Q(VAR)
+400
+100
-500
-1200
-1200
S(VA)
j
Power Δ
P=1600W
θ =-36.87
S=2000VA
2000
b) I = 8.333∠96.87A
ZT = 28.800∠-36.87Ω
c) FP = 0.8leading.
d) inductor L = 0.127H Rating: 240Volts, 1200VA
Q=-1200VAR
Example 7: (based on 2010 final)
For the electric circuit shown below, find: ES, VL, the total power delivered to the load, RL,
and the magnitude of the total impedance seen by the source, |ZS|.
T1
ZS⇒
T2
0.5A ⇒
100Ω
ES
10Ω
+
VL
2:1
RL = 10Ω
3:1
PL = 22.5W
15V = VL;
T1P = 100V;
ZS = 80∠00Ω
Example8: (based on 2010 final)
The voltage source in the following diagram is 120VAC. Each of the two transformers
has a 100 turn centre-tapped primary and secondary (i.e. 50 turns between each of the
terminals on each winding). By making various connections between the source,
transformers and load, different output voltages can be obtained.
120VAC
24Ω
a) List all the possible output voltages that can be obtained by interconnecting the
transformers.
30, 60, 120, 240, 480VAC
b) On the diagram above, draw one connection option, using both transformers, that
would result in 10A being delivered to the 24Ω
load.