This document discusses phasor diagrams and their use in analyzing AC circuits. It begins by defining phasors and explaining that phasor diagrams represent the magnitude and phase of sinusoidal voltages and currents. The document then examines phasor diagrams for pure resistive, inductive, and capacitive circuits. In a pure resistive circuit, the current and voltage are in phase. In a pure inductive circuit, the current lags the voltage by 90 degrees. In a pure capacitive circuit, the current leads the voltage by 90 degrees. Characteristics of each type of circuit are provided along with examples of phasor diagrams.

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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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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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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