1. ELE 102/102Dept of E&E MIT Manipal Phasor Versus Vector: Phasor – defined with respect to time. Vector – defined with respect to space 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. Introduction to Phasors Phasors:

2. ELE 102/102Dept of E&E MIT Manipal The operator ‘j’ : The operator ‘j’ rotates the given vector by 90 degrees in anti-clockwise direction.

3. ELE 102/102Dept of E&E MIT Manipal Phasor representation Rectangular form: Trigonometric Form: Exponential Form: Polar form:

4. ELE 102/102Dept of E&E MIT Manipal Conversion from R ↔ P: Rectangular to Polar: Polar to Rectangular:

5. ELE 102/102Dept of E&E MIT Manipal Conversion from R ↔ P using calculator: Convert the following into polar form using calculator Convert the following into rectangular form using calculator

6. ELE 102/102Dept of E&E MIT Manipal Addition & Subtraction of Phasors Rectangular form is used Addition: (R 1 +jX 1 )+(R 2 +jX 2 ) = (R 1 +R 2 )+j(X 1 +X 2 ) Subtraction: (R 1 +jX 1 )-(R 2 +jX 2 ) = (R 1 -R 2 )+j(X 1 -X 2 )

7. ELE 102/102Dept of E&E MIT Manipal Multiplication & Division of Phasors Polar form is used Multiplication: Division:

8. ELE 102/102Dept 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

9. ELE 102/102Dept of E&E MIT Manipal Rectangular form: Polar form:

10. ELE 102/102Dept of E&E MIT Manipal Graphical Addition of Phasors Phasors are represented in Polar form. Mehod 1: Method 2:

11. ELE 102/102Dept 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.

12. ELE 102/102Dept of E&E MIT Manipal Multiplication and Division are NOT possible using graphical method