ECE 1100: Introduction to Electrical and Computer Engineering Notes 16 Resistors Spring 2011 Wanda Wosik Associate Professor, ECE Dept. Notes prepared by Dr. Jackson

Resistors

Resistors (cont.) R i +- v Note: passive sign convention is assumed here. units of R are Ohms [  ]

Ohm’s Law R i +- v 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.)

Example 10 [  ] 2 [ A ] +- V Find V in each case 10 [  ] 2 [ A ] +- V

Example (cont.) 10 [  ] -2 [ A ] + - V 10 [  ] -2 [ A ] + - V 10 [  ] 2 [ A ] + - V

Power Dissipation R [  ] i + - v Note that passive sign convention is used here. power formula Ohm’s law

Power Dissipation (cont.) i R [  ] + - V Also, so

Example 2 [k  ] [V] Find P abs by resistor Note: in the MKS system, we must use [V], [A], [  ], [W], [J].

Example Find power P abs ( t ) absorbed by resistor R = 144 [  ] + - v ( t ) Find average power P abs AVE absorbed by resistor (60 [Hz] AC line voltage)

Example (cont.) P abs ( t ) T p = T / 2 = 0.5 ( 1/60 ) [s] t R = 144 [  ] + - v ( t ) T = 1 / f = 1/60 [s] cos (  t ) t

Example (cont.) + - v ( t ) P abs ( t ) T p = 0.5 (1/60) = 1/120 [s] = [s] t

Example (cont.) Note: cos 2 (  t ) = ½ + ½ cos(2  t) Note: the average value of cos 2 (  t) is ½.

Example (cont.) R = 144 [  ] What is this? A 100 [W] light bulb! (60 Hz AC line voltage)

Example (cont.) R = 144 [  ] 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.) General Formula The RMS voltage is the peak voltage divided by  2.