L18 1 ph-ac

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ELE 102/102 Dept of E&E MIT Manipal 1 Introduction to Phasors v(wt) = V m sin wt v() = V m sin t v V m 0 V m V m -V m 0 N S a b Coil Rotation A phasor is a graphical representation of the magnitude and angular position of a time varying quantity such as a voltage or current in which variation is sinusoidal. A phasor diagram can be used to show the relative relationship of two or more sine waves of the same frequency.

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Transcript of L18 1 ph-ac

Page 1: L18 1 ph-ac

ELE 102/102 Dept of E&E MIT Manipal 1

Introduction to Phasors

v(wt) = Vm sin wtv() = Vm sin

t

v Vm

0

Vm

Vm

-Vm

0

N S

a

b Coil

Rotation

A phasor is a graphical representation of the magnitude and angular

position of a time varying quantity such as a voltage or current in

which variation is sinusoidal.

A phasor diagram can be used to show the relative relationship of two

or more sine waves of the same frequency.

Page 2: L18 1 ph-ac

ELE 102/102 Dept of E&E MIT Manipal

The operator ‘j’ :

The operator ‘j’ rotates the given vector by 90 degrees in anti-clockwise direction.

jAAj )(

AAjjAj 2)(

1j 1;j Therefore, 2

RefA

jA

Aj2

jAAj3

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ELE 102/102 Dept of E&E MIT Manipal

Phasor representation

Rectangular form:

Trigonometric Form:

Exponential Form:

Polar form:

jXRA

SinAjCosAA ||||

jeAA ||

|| AA

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ELE 102/102 Dept of E&E MIT Manipal

Conversion from R ↔ P:

R

Xtanθ

;XR|A|

1

22

Rectangular to Polar:

Polar to Rectangular:

sin||

cos||

AX

AR

Page 5: L18 1 ph-ac

ELE 102/102 Dept of E&E MIT Manipal

Conversion from R ↔ P using calculator:

Convert the following into polar form using calculator

j6-8 3)

j68 2)

j4 31

)

36.87-10

36.87 10

53.135

4510)3

603)2

305)1

07.7j07.7

59.2j5.1

5.2j33.4

Convert the following into rectangular form using calculator

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ELE 102/102 Dept of E&E MIT Manipal

Addition & Subtraction of Phasors

Rectangular form is used

Addition:

(R1+jX1)+(R2+jX2) = (R1+R2)+j(X1+X2)

Subtraction:

(R1+jX1)-(R2+jX2) = (R1-R2)+j(X1-X2)

Page 7: L18 1 ph-ac

ELE 102/102 Dept of E&E MIT Manipal

Multiplication & Division of Phasors

Polar form is used

Multiplication:

Division:

)(|]|*|[|||*|| 21212211 AAAA

)(||

||

||

||21

2

1

22

11

A

A

A

A

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ELE 102/102 Dept of E&E MIT Manipal

A phasor diagram can be used to show the relative

relationship of two or more sine waves of the same

frequency.

Graphical Representation of Phasors

Real

A

B

C

O

Imaginary

A phasor can be resolved into two components at right angles to each other.

OA is a phasor.

Horizontal component = OB

Vertical component OC = AB

OA = OB + jOC = R + jX

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ELE 102/102 Dept of E&E MIT Manipal

Rectangular form:

Polar form:

jXRA

|| AA

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ELE 102/102 Dept of E&E MIT Manipal

Graphical Addition of Phasors

Phasors are represented in Polar form.

Mehod 1:

Method 2:

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ELE 102/102 Dept of E&E MIT Manipal

Graphical Subtraction of Phasors

Phasors are represented in Polar form.

The Second phasor is reversed and added with the first phasor.

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ELE 102/102 Dept of E&E MIT Manipal

Multiplication and Division are

NOT possible

using graphical method