ECE 1100: Introduction toECE 1100: Introduction toElectrical and Computer EngineeringElectrical and Computer Engineering

Notes 16

Resistors

Spring 2011

Wanda WosikAssociate Professor, ECE Dept.

Notes prepared by Dr. Jackson

ResistorsResistors

Resistors (cont.)Resistors (cont.)

Ri

+ -v

Note: passive sign convention is assumed here.

vR

i

v Ri

units of R are Ohms []

Ohm’s LawOhm’s Law

Ri

+ -v

v Ri i

v

There is a linear relationship between voltage and current. (That is, the value of R does not depend on the current going through it.)

ExampleExample

10 []2 [A]

+ -V

Find V in each case

10 2 20 [V]V RI

10 []2 [A]

+ -V

10 2 20 [V]V RI

Example (cont.)Example (cont.)

10 []-2 [A]

+- V

10 2 20 [V]V RI

10 []-2 [A]

+- V

10 2 20 [V]V RI

10 []2 [A]

+- V

10 2 20 [V]V RI

Power DissipationPower Dissipation

R []i

+ -v

2

absP vi

Ri i

Ri

Note that passive sign convention is used here.

power formula Ohm’s law

Power Dissipation (cont.)Power Dissipation (cont.)i R []

+ -V

2absP Ri

Also,

2

abs

vP R

R

so2

abs

vP

R

ExampleExample

2 [k]

-+

12 [V]

Find Pabs by resistor

22

3

120 072

2 10abs

VP .

R

0 072 [W]

(72 [mW])absP .

Note: in the MKS system, we must use [V], [A], [], [W], [J].

ExampleExample

Find power Pabs (t) absorbed by resistor

22

2120 2cos 2 60

200cos 2 60144abs

tv tP t t

R

R = 144 []+-v (t)

Find average power PabsAVE

absorbed by resistor

120 2cos 2 60 [V]v t t

(60 [Hz] AC line voltage)

Example (cont.) Example (cont.)

2200cos 2 60 [W]absP t t

Pabs (t)

Tp = T/2 = 0.5 (1/60) [s]t

R = 144 []+-v (t)

T = 1 / f = 1/60 [s]co

s (

t)

t

Example (cont.) Example (cont.)

0

1 pT

AVEabs abs

p

P P t dtT

+-v (t)

2200cos 2 60 [W]absP t t

2

0

1200cos 2 60

pT

AVEabs

p

P t dtT

Pabs (t)

Tp= 0.5 (1/60) = 1/120 [s] = 0.00833 [s]t

Example (cont.)Example (cont.)

1 1202

0

1 1202

0

1200cos 2 60

1 120

200 120 cos 2 60

/AVE

abs

/

P t dt/

t dt

Note: cos2 (t) = ½ + ½ cos(2t)

1 120

0

sin 2 2 601200 120

2 2 2 2 60

1 120200 120 100

2

/

AVEabs

* ttP

*

/

Note: the average value of cos2 (t) is ½.

Example (cont.)Example (cont.)

100 [W]AVEabsP

120 2cos 2 60 [V]v t t

R = 144 []

What is this? A 100 [W] light bulb!

(60 Hz AC line voltage)

Example (cont.)Example (cont.)

2 2120 120

100 [W]144

AVEabsP

R

120 2cos 2 60 [V]v t t

R = 144 []

2 2

120 2 120 2200 [W]

144AVE

absPR

Observation about average power:

The value 120 [V] is called the effective or RMS (Root Mean Square) voltage.(The meaning of the term “RMS” will become clear in later notes.)

Example (cont.)Example (cont.)

2RMS

AV

cos [V]v t A t

General Formula

2

RMSAVEabs

VP

R

The RMS voltage is the peak voltage divided by 2.