Chapter-7

Chapter-7 - Univ. of Ontario Institute of Technology '...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Univ. of Ontario Institute of Technology Faculty of Engineering and Applied Science ' $ % AC Power We have learned so far that in an electric circuit that is excited by a sinusoidal source, all the voltages and currents in the circuit are also sinusoidals of the same frequency. Consider the following circuit. Electric Circuits (ENGR2790U) 217 of 310
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
AC Power ' $ % Electric Circuits (ENGR2790U) 218 of 310
Background image of page 2
AC Power ' $ % The voltage and current delivered to an arbitrary load can be written in the general forms: v ( t ) = V cos( ωt ) i ( t ) = I cos( ωt - θ I ) where V / I is the peak amplitudes of the sinusoidal voltage/current, and θ I is the phase delay of current with respect to the voltage. Then the instantaneous power dissipated by the load is given by p ( t ) = v ( t ) i ( t ) = V I cos( ωt ) cos( ωt - θ ) Electric Circuits (ENGR2790U) 219 of 310
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
AC Power ' $ % Using trigonometric identities, we can write the instantaneous power as p ( t ) = V I 2 cos( θ ) | {z } Constant + V I 2 cos(2 ωt - θ ) | {z } time-varying As can be seen, the instantaneous power dissipated by the load has an average component and a sinusoidal component. Electric Circuits (ENGR2790U) 220 of 310
Background image of page 4
AC Power ' $ % Electric Circuits (ENGR2790U) 221 of 310
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
AC Power ' $ % Electric Circuits (ENGR2790U) 222 of 310
Background image of page 6
AC Power ' $ % The average power P av is obtained as P av = 1 T Z T 0 p ( t ) dt = 1 T Z T 0 V I 2 cos θdt + 1 T Z T 0 V I 2 cos(2 ωt - θ ) dt = V I 2 cos θ (3) Note that Z ( ) = V ( ) I ( ) = V e j 0 Ie - = V I e = | Z | e Electric Circuits (ENGR2790U) 223 of 310
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
AC Power ' $ % Then, we can the average power as P av = 1 2 V 2 | Z | cos θ = 1 2 I 2 | Z | cos θ In North America, AC frequency is ω = 2 π 60 = 377 rad / s In Europe ω = 2 π 50 = 314 rad / s Electric Circuits (ENGR2790U) 224 of 310
Background image of page 8
AC Power ' $ % Using rms values V rms = V 2 = ˜ V I rms = I 2 = ˜ I we can write the average power as P av = 1 2 V 2 | Z | cos θ = ˜ V 2 | Z | cos θ = 1 2 I 2 | Z | cos θ = ˜ I 2 | Z | cos θ = ˜ V ˜ I cos θ (4) Electric Circuits (ENGR2790U) 225 of 310
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
AC Power ' $ % We denote the rms phasors as ˜ V = V rms e V = ˜ V e V = ˜ V θ V ˜ I = I rms e I = ˜ Ie I = ˜ I θ I Example 7.1: Electric Circuits (ENGR2790U) 226 of 310
Background image of page 10
AC Power ' $ % Example 7.2: Electric Circuits (ENGR2790U) 227 of 310
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Univ. of Ontario Institute of Technology Faculty of Engineering and Applied Science ' $ % Complex Power Complex power is defined a S = ˜ V ˜ I * Not that S = ˜ V ˜ I cos θ | {z
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/18/2010 for the course MATH 2860 taught by Professor Dhavidhe during the Spring '10 term at UOIT.

Page1 / 46

Chapter-7 - Univ. of Ontario Institute of Technology '...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online