Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

1Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

2Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

3Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

4Circuits II EECE 2020Phasors - Intro

“f” is also known as “cycles per second”“t” is known as “seconds per cycle”

“f” is the “cyclic frequency”“ω” is the “angular frequency”

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

5Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

6Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

7Circuits II EECE 2020Phasors - Intro

Head start => It “leads”!

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

8Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

9Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

10Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

11Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

12Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

13Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

14Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

15Circuits II EECE 2020Phasors - Intro

All 4 statements say the same thing in slightly different ways.

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

16Circuits II EECE 2020Phasors - Intro

10mS happens to be exactly 1 cycle!

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

17Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

18Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

19Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

20Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

21Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

22Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

23Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

24Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

25Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

26Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

27Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

28Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

29Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

30Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

31Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

32Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

33Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

34Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

35Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

36Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

37Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

38Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

39Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

40Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

41Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

42Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

43Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

44Circuits II EECE 2020Phasors - Intro

Phasors - Intro

University of Massachusetts, Lowell

301 Ball Hall

One University Avenue

Lowell, Massachusetts 01854

Phone: (978) 934-3300

Fax: (978) 934-3027

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

45Circuits II EECE 2020Phasors - Intro