Ee1 chapter12 phasor_diagram

Apr 12, 2023

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Contact Number

IT2001PAEngineering Essentials (1/2)

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.



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



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



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



Phasor Diagram

There are three ways to describe the phase angle in a phasor diagram:

1. Same phase or in phase2. Leading3. Lagging



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



Leading Phase Angle

I leads V by 45o.

Equation:v = Vm sin i = Im sin ( + 45o)



Lagging Phase Angle

V lags I by 90o.

Equation:i = Im sin v = Vm sin ( - 90o )



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



Inductors and Inductance

Inductor's emf opposes change in current



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




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




Click next to continue

Sinusoidal waveform of a pure resistive circuit

Applied voltage ( V ) is IN PHASE with the current ( I )

VI




Formula for the pure resistive circuit

V = I R V I = ---- R

V R = ---- I



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 )




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





Sinusoidal waveform of a pure inductive circuit

Applied voltage (V ) is leading the current ( I ) by 90°

VI

90°





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 )



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 )



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




22

Sinusoidal waveform of a pure capacitive circuit

Current ( I ) is LEADING the Applied voltage (V ) by 90°

VI

90°





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 )



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



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



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



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



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



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



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



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



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



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



Summary

Phasor Diagrams Phase shift, phase angle, characteristics of

Purely resistive circuit Purely capacitive circuit Purely inductive circuit



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