1. IT2001PA
Engineering Essentials (1/2)
Chapter 12 – Phasor Diagram
Lecturer Name
lecturer_email@ite.edu.sg
Sep 4, 2012
Contact Number

2. Chapter 12 – Phasor Diagram
Lesson Objectives
Upon completion of this topic, you should be able to:
 Explain what is a phasor diagram.
 Explain and determine the characteristics of a pure
resistive, pure inductive and pure capacitive circuit.
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IT2001PA Engineering Essentials (1/2)

3. Chapter 12 – Phasor Diagram
Phasor
 Used to represent sinusoidal
functions.
 Useful in showing the relationship Vm
over time of various quantities v 2πft +φ
(such as current and voltage).
 A phasor is a vector (i.e. described
by polar coordinates length and
angle) with
 length equal to amplitude of
function (Vm) v = Vmsin(2πft+φ)
 angle equal to argument (θ)
 height equal to value of function
(φ)
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4. Chapter 12 – Phasor Diagram
Phasor Diagram
It is a diagram that represent graphically the magnitude and
phase of a sinusoidal alternating current or voltage.
Phasor
Waveform
Phase angle (ϕ) is the angle by which the voltage and
current phasors are displaced with respect to each
other.
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5. Chapter 12 – Phasor Diagram
Phase Difference
Vm1
v1 = Vm1sin(2πft+φ1)
ϕ 2- ϕ 1
v2 = Vm2sin(2πft+φ2) Vm2
 The two functions differ in
 their amplitudes and;
 their phase constants, φ1 and
φ 2.
 The functions have a phase
difference of φ2 − φ1.
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6. Chapter 12 – Phasor Diagram
Phasor Diagram
There are three ways to describe the phase angle in
a phasor diagram:
1. Same phase or in phase
2. Leading
3. Lagging
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7. Chapter 12 – Phasor Diagram
Same Phase or In Phase
V and I are in phase.
The equation to represent the voltage and current
waveforms are:
θ=2πft
v = Vm sin θ
Φ=0°
i = Im sin θ
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8. Chapter 12 – Phasor Diagram
Leading Phase Angle
I leads V by 45o.
Equation:
v = Vm sin θ
i = Im sin (θ + 45o)
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9. Chapter 12 – Phasor Diagram
Lagging Phase Angle
V lags I by 90o.
Equation:
i = Im sin θ
v = Vm sin (θ - 90o )
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10. Chapter 12 – Phasor Diagram
Inductor
 Passive electrical device that stores energy
in a magnetic field, by combining the effects
of many loops of electric current
 Change in current will induce a an
opposing emf in an inductor
 Inductance L is a physical characteristic of
an inductor (unit is Henry, H).
 Inductance relates the induced emf of an
inductor to the rate of change of current
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11. Chapter 12 – Phasor Diagram
Inductors and Inductance
Inductor's emf opposes change in current
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12. Chapter 12 – Phasor Diagram
Pure Resistive Circuit
Characteristics of A.C. Pure Resistive Circuit
Voltage and current are equally opposed by the circuit.
The current flows through the resistor is in-phase with the
applied voltage.
The phase angle between the applied voltage and current is 0°
R
I I V
V
Circuit Diagram Phasor Diagram
Click next to continue 12
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13. Chapter 12 – Phasor Diagram
Pure Resistive Circuit
 The voltage across the
resistor oscillates in
phase with the emf of AC
generator.
 Current and voltage
across the resistor are in
phase:
 They peak and trough at
the same time, and both
are zero at the same
times as well
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IT2001PA Engineering Essentials (1/2)

14. Chapter 12 – Phasor Diagram
Pure Resistive Circuit
Sinusoidal waveform of a pure resistive circuit
Applied voltage ( V ) is IN PHASE with the current ( I )
V
I
φ
Click next to continue
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15. Chapter 12 – Phasor Diagram
Pure Resistive Circuit
Formula for the pure resistive circuit
V V
V=I× R
I = ---- R = ----
R I
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16. Chapter 12 – Phasor Diagram
Pure Inductive Circuit
Characteristics of A.C. Pure Inductive Circuit
There is opposition to current flow.
Current flows through the pure inductor lags the applied voltage by
90°.
The phase angle between the applied voltage and current is 90°. ( φ=
90° )
L : inductance in Henry ( H )
L V
90°
I
V I
Circuit Diagram Phasor Diagram
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17. Chapter 12 – Phasor Diagram
Pure Inductive Circuit
 Induced emf of the
inductor is oriented
so it opposes the
change in current.
 Rate of change of
current determines
the voltage.
 Current lags voltage
by 90°
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18. Chapter 12 – Phasor Diagram
Pure Inductive Circuit
Sinusoidal waveform of a pure inductive circuit
Applied voltage (V ) is leading the current ( I ) by 90°
V
I
90°
φ
Click next to continue 18
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19. Chapter 12 – Phasor Diagram
Pure Inductive Circuit
In a pure inductive circuit, the opposition to the current flow
is called the inductive reactance.
Symbol : XL
Unit : Ohms ( Ω )
XL = 2 π f L V
XL = ---
f = frequency in Hertz ( Hz ) I
L = inductance in Henry ( H )
Click next to continue 19
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20. Chapter 12 – Phasor Diagram
Pure Capacitive Circuit
Characteristics of A.C. Pure Capacitive Circuit
Current flows through the pure capacitor leads the applied
voltage by 90°.
The phase angle between the applied voltage and current is 90°.
( φ= 90° )
C = capacitance in Farad ( F )
C I
I
90°
V V
Circuit Diagram Phasor Diagram
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21. Chapter 12 – Phasor Diagram
Pure Capacitive Circuit
 Current starts at a maximum
while the voltage across the
capacitor is zero, since it is
initially uncharged
 When the current reaches
zero, the capacitor plates are
fully charged, and the
magnitude of the voltage
across it is at a maximum
 The current reaches a peak
earlier in time than the
potential difference does.
 Current leads voltage by 90°
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22. Chapter 12 – Phasor Diagram
Pure Capacitive Circuit
Sinusoidal waveform of a pure capacitive circuit
Current ( I ) is LEADING the Applied voltage (V ) by 90°
V
I
90°
φ
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23. Chapter 12 – Phasor Diagram
Pure Capacitive Circuit
In a pure capacitive circuit, the opposition to the voltage
is called the capacitive reactance.
Symbol : Xc
Unit : Ohms ( Ω )
1 V
Xc = --------- Xc = ---
2π f C I
f = frequency in Hertz ( Hz )
Click next = capacitance in Farad ( F )
C to continue 23
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24. Chapter 12 – Phasor Diagram
Quiz
1. The diagram shows the phasor diagram of the
I V
A. Pure capacitive circuit
B. Pure resistive circuit
C. Pure inductive circuit
D. Resistor-inductor series circuit
Ans : B
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25. Chapter 12 – Phasor Diagram
Quiz
2. The phase angle between the applied voltage and the
current in an A.C. pure resistive circuit is
A. 0°
B. 30°
C. 45°
D. 90°
Ans : A
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26. Chapter 12 – Phasor Diagram
Quiz
3. In the pure inductive circuit the current
A. Is in phase with the applied voltage
B. Leads the applied voltage by 90°
C. Lags the applied voltage by 45°
D. Lags the applied voltage by 90°
Ans : D
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27. Chapter 12 – Phasor Diagram
Quiz
4. The inductive reactance is represented by an equation :
A. XL = 2 f L
B. XL = 2 πf L
C. XL = V f L
1
D. XL = --------
2πfL Ans : B
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28. Chapter 12 – Phasor Diagram
Quiz
5. Which is the correct phasor diagram of an A.C.
pure capacitive circuit?.
I
A. I V C
V
.
V I
B D
I V
. .
Ans : D
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29. Chapter 12 – Phasor Diagram
Quiz
6. The opposition to the current flow in a pure
capacitive circuit is called
A. Impedance
B. Resistance
C. Inductive reactance
D. Capacitive reactance
Ans : D
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30. Chapter 12 – Phasor Diagram
Quiz
7. The capacitive reactance is represented by an equation :
A. Xc = 2 π C
B. Xc = 2 π f C
1
C. Xc = ---------
2fC
1
D. Xc = ---------
2πfC Ans : D
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31. Chapter 12 – Phasor Diagram
Quiz
8. The current flow in an A.C. pure inductive circuit can be
calculated using a formula :
V
A. I = ----
R
V
B. I = -----
XL
V
C. I = -----
Xc
D. I = V XL
Ans : B
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32. Chapter 12 – Phasor Diagram
Quiz
9. The sinusoidal waveform V
of an A.C. circuit shows I
that the
90°
φ
A. Applied voltage is in phase B. Applied voltage is lagging
with the current the current by 90°
D. Current is leading the
C. Applied voltage is leading
applied voltage by 90°
the current by 90°
Ans : C
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33. Chapter 12 – Phasor Diagram
Quiz
10. The diagram shows an V
A.C. sinusoidal waveform I
of a
φ
A. Pure resistive circuit C. Pure capacitive circuit
B. Pure inductive circuit D. Resistor-Capacitor series
circuit
Ans : A
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34. Chapter 12 – Phasor Diagram
Summary
 Phasor Diagrams
 Phase shift, phase angle, characteristics of
 Purely resistive circuit
 Purely capacitive circuit
 Purely inductive circuit
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35. Chapter 12 – Phasor Diagram
Next Lesson
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