Download Tutorial 2 (AC Fundamentals)

TUTORIAL 2
AC Fundamentals
1. The voltage across a component is described by the equation: v(t) = 120 sin (1000t). The
current flowing through the component is described by the equation: i(t) = 3 sin (1000t +
30),
a)
What is the frequency of the voltage?
b)
What is the peak value of the current?
c)
What is the RMS value of the voltage?
d)
What is the phase angle between the voltage and the current?
e)
Does the current lead or lag the voltage
f)
What is the impedance of the component?
Answers a) 159 Hz, b) 3 A, c) 84.9 V, d) 300, e) Leads, f) 40∠-300
2. A voltage of 500 V is measured across a capacitor when a sinusoidal current of 1 A at a
frequency of 1000 Hz passes through it.
a)
What is the reactance of the capacitor at 1000Hz?
b)
What is the value of the capacitance?
c)
What voltage would you expect to see appearing across the capacitor if the
frequency of the current is reduced to 200 Hz?
Answers a) 500Ω, b) 0.318 µF, c) 2.5 kV
3. The current in an inductor is measured as 0.5 A when a sinusoidal voltage of 75 V at a
frequency of 50 Hz is applied across it.
a)
What is the reactance of the inductor?
b)
What is the value of the inductance?
c)
What current would be observed in the frequency of the voltage was changed to
125 Hz?
Answers a) 150 Ω, b) 0.48 H, c) 0.2 A
By Haziah Abdul Hamid (PPKSE)
4. A coil with a resistance of 10Ω and an inductance of 0.2H is connected to a 100V, 50Hz
supply, calculate:
a)
The reactance of the coil
b)
The magnitude of the impedance of the coil.
c)
The current flowing in the coil
d)
The phase difference between the current and the applied voltage
Answers a) 62.8 Ω, b) 63.6Ω, c) 1.57A d) 80.950
5. Three circuit elements are connected in series and the voltages across the circuit elements
are given by:
v1 =50 sin (ωt),
v2 =40 sin (ωt + 60) and
v3 =60 sin (ωt-30)
Calculate the total voltage appearing across the three components and its phase angle
with reference to v1.
Answer 1222.17 V
6. Two coils (i.e. coil 1 and coil 2) are connected in series. With a 2A d.c. current flowing
through the circuit, potential differences of 20V and 30V appear across the coils
respectively. With a 2 A a.c. current flowing through the circuit at a frequency of 40Hz the
potential different become 140V and 100V.
a)
Calculate the resistances associated with each coil
b)
Calculate the magnitude of the impedance of each coil
c)
Calculate the reactance associated with each coil
d)
Calculate the inductance associated with each coil
Answers a) R1= 10Ω, R2= 15Ω b) Z1=70Ω, Z2=50Ω, c) X1=69.3Ω,
X2=47.6Ω, d) L1=0.28H, L2=0.19H
7. If the two coils in question 6 are connected in series to a 230V, 50Hz supply calculate
a)
The current
b)
The phase angle between the voltage and the current
By Haziah Abdul Hamid (PPKSE)
c)
Draw the complete phasor diagram for the circuit.
Answers a) 1.53A, b) 80.40 lag
8. A relay coil has an inductance of 8mH and a resistance of 30Ω. An alternating voltage v =
5 sin (5000t) is applied to the coil.
a)
What is the frequency of the current flowing in the coil?
b)
What is the R.M.S. value of the current
c)
Express the current in the form i(t) = Imax sin(ωt - φ) (φ in radians)
d)
Find the maximum rate of change of the current
e)
What is magnitude of the applied voltage when the rate of change of current is
at its maximum?
Answers a) 796 Hz, b) 0.0707A, c) 0.1 sin(5000t-0.927)A, d)500 A/sec e 4V
By Haziah Abdul Hamid (PPKSE)
AC Steady State
1. Determine i in the circuit of Fig. 1.
Figure 1
2. Determine i1 in the circuit of Fig. 2.
Figure 2
3. Use source transformation to find vo in the circuit of Fig. 3.
Figure 3
4. For the circuit depicted in Fig. 4, find the Thevenin equivalent circuit at terminals a-b.
Figure 4
5. Find the Thevenin and Norton equivalent circuits at terminals a-b for each of the circuits in
Fig. 5(a) and (b)
Figure 5(a)
By Haziah Abdul Hamid (PPKSE)
Figure 5(b)
6. Find the Thevenin and Norton equivalent circuits for the circuit shown in Fig. 6
Figure 6
7. Calculate v o (t) in the circuit of Fig. 7
Fig 7
8. Given the circuit in Fig. 8, find the average power supplied or absorbed by each element.
Fig 8
9. Assuming that v s = 8 cos(2t – 40º) V in the circuit of Fig. 9, find the average power
delivered to each of the passive elements.
Fig 9
10. Obtain the power factor for each of the circuits in Fig. 10. Specify each power factor as
leading or lagging.
By Haziah Abdul Hamid (PPKSE)
Fig 10.
By Haziah Abdul Hamid (PPKSE)