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Apr 12, 2023
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IT2001PAEngineering Essentials (1/2)
Chapter 12 – Phasor Diagram
Chapter 12 – Phasor Diagram
IT2001PA Engineering Essentials (1/2) 2
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.
Chapter 12 – Phasor Diagram
IT2001PA Engineering Essentials (1/2) 3
Phasor
Used to represent sinusoidal functions.
Useful in showing the relationship over time of various quantities (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)
angle equal to argument () height equal to value of function
(φ)
v = Vmsin(2ft+φ)
Vm
2ft +φv
Chapter 12 – Phasor Diagram
IT2001PA Engineering Essentials (1/2) 4
Phasor Diagram
It is a diagram that represent graphically the magnitude and phase of a sinusoidal alternating current or voltage.
Phase angle () is the angle by which the voltage and current phasors are displaced with respect to each other.
Waveform
Phasor
Chapter 12 – Phasor Diagram
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Phase Difference
The two functions differ in their amplitudes and;
their phase constants, φ1 and φ2.
The functions have a phase difference of φ2 − φ1.
v1 = Vm1sin(2ft+φ1)
v2 = Vm2sin(2ft+φ2)2- 1
Vm1
Vm2
Chapter 12 – Phasor Diagram
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Phasor Diagram
There are three ways to describe the phase angle in a phasor diagram:
1. Same phase or in phase2. Leading3. Lagging
Chapter 12 – Phasor Diagram
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Same Phase or In Phase
V and I are in phase.
The equation to represent the voltage and current waveforms are:
v = Vm sin i = Im sin
=2ft
Φ=0
Chapter 12 – Phasor Diagram
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Leading Phase Angle
I leads V by 45o.
Equation:v = Vm sin i = Im sin ( + 45o)
Chapter 12 – Phasor Diagram
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Lagging Phase Angle
V lags I by 90o.
Equation:i = Im sin v = Vm sin ( - 90o )
Chapter 12 – Phasor Diagram
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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
Chapter 12 – Phasor Diagram
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Inductors and Inductance
Inductor's emf opposes change in current
Chapter 12 – Phasor Diagram
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Pure Resistive Circuit
12Click next to continue
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°
VI
R
V
I
Circuit Diagram Phasor Diagram
Chapter 12 – Phasor Diagram
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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
Chapter 12 – Phasor Diagram
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Pure Resistive Circuit
Click next to continue
Sinusoidal waveform of a pure resistive circuit
Applied voltage ( V ) is IN PHASE with the current ( I )
VI
Chapter 12 – Phasor Diagram
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Pure Resistive Circuit
Formula for the pure resistive circuit
V = I R V I = ---- R
V R = ---- I
Chapter 12 – Phasor Diagram
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Pure Inductive Circuit
16
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°. ( = 90° )
V
I
90
V
L
I
Circuit Diagram Phasor Diagram
L : inductance in Henry ( H )
Chapter 12 – Phasor Diagram
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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
Chapter 12 – Phasor Diagram
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Pure Inductive Circuit
18Click next to continue
Sinusoidal waveform of a pure inductive circuit
Applied voltage (V ) is leading the current ( I ) by 90°
VI
90°
Chapter 12 – Phasor Diagram
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Pure Inductive Circuit
19Click next to continue
In a pure inductive circuit, the opposition to the current flow is called the inductive reactance. Symbol : XL Unit : Ohms ( )
XL = 2 f L V XL = --- If = frequency in Hertz ( Hz )
L = inductance in Henry ( H )
Chapter 12 – Phasor Diagram
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Pure Capacitive CircuitCharacteristics 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°. ( = 90° )
V
I
90
Phasor DiagramCircuit Diagram
V
C
I
C = capacitance in Farad ( F )
Chapter 12 – Phasor Diagram
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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
Chapter 12 – Phasor Diagram
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Pure Capacitive Circuit
22
Sinusoidal waveform of a pure capacitive circuit
Current ( I ) is LEADING the Applied voltage (V ) by 90°
VI
90°
Chapter 12 – Phasor Diagram
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Pure Capacitive Circuit
23Click next to continue
In a pure capacitive circuit, the opposition to the voltage is called the capacitive reactance. Symbol : XcUnit : Ohms ( )
1Xc = --------- 2 f C
V Xc = --- I
f = frequency in Hertz ( Hz ) C = capacitance in Farad ( F )
Chapter 12 – Phasor Diagram
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Quiz
1. The diagram shows the phasor diagram of the
A. Pure capacitive circuit
B. Pure resistive circuit
C. Pure inductive circuit
D. Resistor-inductor series circuit
VI
Ans : B
Chapter 12 – Phasor Diagram
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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
Chapter 12 – Phasor Diagram
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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
Chapter 12 – Phasor Diagram
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Quiz
4. The inductive reactance is represented by an equation :
A. XL = 2 f L
B. XL = 2 f L
C. XL = V f L
1 D. XL = --------
2 f L Ans : B
Chapter 12 – Phasor Diagram
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Quiz
5. Which is the correct phasor diagram of an A.C. pure capacitive circuit?.
A.
I V
B.
I
V
C.
I
V
D.
I
V
Ans : D
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Quiz
C. Inductive reactance
B. Resistance
A. Impedance
D. Capacitive reactance
6. The opposition to the current flow in a pure capacitive circuit is called
Ans : D
Chapter 12 – Phasor Diagram
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Quiz
A. Xc = 2 C
B. Xc = 2 f C
1 C. Xc = --------- 2 f C
1 D. Xc = --------- 2 f C
7. The capacitive reactance is represented by an equation :
Ans : D
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Quiz
V A. I = ---- R
V B. I = ----- XL
D. I = V XL
V C. I = ----- Xc
8. The current flow in an A.C. pure inductive circuit can be calculated using a formula :
Ans : B
Chapter 12 – Phasor Diagram
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Quiz
A. Applied voltage is in phase with the current
B. Applied voltage is lagging the current by 90°
D. Current is leading the applied voltage by 90°
C. Applied voltage is leading the current by 90°
9. The sinusoidal waveform of an A.C. circuit shows that the
VI
90°
Ans : C
Chapter 12 – Phasor Diagram
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Quiz
A. Pure resistive circuit
B. Pure inductive circuit
C. Pure capacitive circuit
D. Resistor-Capacitor series circuit
10. The diagram shows an A.C. sinusoidal waveform of a
VI
Ans : A
Chapter 12 – Phasor Diagram
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Summary
Phasor Diagrams Phase shift, phase angle, characteristics of
Purely resistive circuit Purely capacitive circuit Purely inductive circuit
Chapter 12 – Phasor Diagram
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