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Tutorial 8 – AC Fundamentals
TUTORIAL 8
AC FUNDAMENTALS
1. Express each of the following as an angle between -180 and +180.
a) 200
b) -190
c) 280
d) 380
e) -270
f) 940
2. Find the average value of each of the waveforms shown below.
v(t)
8V
0.1
0.3
0.5
0.7
t(ms)
-8V
i(t)
+5A
1.5 2.0
0.5 1.0
3.5 4.0
2.5 3.0
5.5
4.5 5.0
t(s)
-3A
v(t)
+30mV
1
2 2.5
3.5
4.5 5
6
7 7.5
t(μs)
+100mA
27
7
5
-50mA
EE1404 Circuit Theory
Dr. Daniel Nankoo
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16 20
25
31
29
36 40
t(ms)
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Tutorial 8 – AC Fundamentals
3. Find the average value of v(t) = 6 + 2sin(2  100t)V. Sketch the waveform.
Label the minimum and maximum values.
4. Find the effective value of each of the following.
a) i(t) = 100sin(3840t) A
b) v(t) = 260sin(t - 30) mV
c) i(t) = (2)cos(104t) A
d) v(t) = 0.13sin(t + 120) V
5. Find the peak value of a sinusoidal waveform whose rms value is
a) 1.2V rms
b) 39 A rms
c) 480 nV rms
d) 7.5 A rms
6. Find the effective value of each of the waveforms shown below.
v(t)
+5V
0.2
0.4
0.6
0.8
1.0
1.2
1.4
t(s)
-10V
T(ms)
i(t)
0.3A
0.1
1.1
1
2.1
2
3.1
3
4.1
4
5.1
5
t(s)
7. Write the mathematical expression for the current through a 2k resistor
when the voltage across it is
a) v(t) = 18sin(400t) V
b) v(t) = 840sin(t + 30) mV
c) v(t) = 0.5cos(2  105t - 80) V
d) v(t) = -sin(1832t + 100) V
EE1404 Circuit Theory
Dr. Daniel Nankoo
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Tutorial 8 – AC Fundamentals
8. Write the mathematical expression for the voltage across a 120 resistor
when the current through it is
a) i(t) = 0.1sin(377t) A
b) i(t) = 42sin(2  60t + 45) mA
c) i(t) = cos(t) A
d) i(t) = -185sin(9841t - 70) A
9. Find the capacitive reactance of
a) a 0.1F capacitor when the frequency of the current through it is 4.6kHz
b) a 150F capacitor when the voltage across it is 16sin(5000t) V
c) a 20pF capacitor when the current through it is 95sin(2  4  106t) A
d) a 0.022F capacitor at DC.
10. Find the peak current through a 0.01F capacitor when the voltage across
it is
a) v(t) = 4sin(106t - 45) V
b) v(t) = 169sin(377t) V
c) v(t) = 100cos(2  104t - 80) V
11. Find the inductive reactance of
a) a 20mH inductor when the current through it has a frequency of 40kHz
b) a 1.5H inductor when the voltage across it is 65sin(320t) mV
c) a 400H inductor when the current through it is 128sin(2  107t - 50) mA
d) a 0.06H inductor at DC.
12. Find the peak current through a 0.04H inductor when the voltage across it
is
a) v(t) = 5sin(1800t) V
b) v(t) = 40sin(2  100t + 40) V
c) v(t) = 0.1sin(105t + 70) V
13. The current through a 150 resistor is i(t) = 24sin(377t) mA. Find the
average power dissipated in the resistor.
14. The average power dissipated by a 100 resistor is 1.5W. Assuming that
the AC voltage across the resistor is sinusoidal:
a) Find the effective value of the voltage across the resistor.
b) Find the peak value of the current through the resistor.
EE1404 Circuit Theory
Dr. Daniel Nankoo
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