Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz

Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 16 CHAPTER Alternating Voltage and Current

Topics Covered in Chapter 16  Alternating Current Applications  Alternating-Voltage Generator  The Sine Wave  Alternating Current  Voltage and Current Values for a Sine Wave

Topics Covered in Chapter 16 (continued)  Frequency  Period and Wavelength  Phase Angle  The Time Factor in Frequency and Phase  AC Circuits with Resistance

Topics Covered in Chapter 16 (continued)  Nonsinusoidal AC Waveforms  Harmonic Frequencies  The 60-Hz AC Power Line  Motors and Generators  Three-Phase AC Power

N S + V - V A loop rotating in a magnetic field generates a sine wave. 0  V instantaneous = V max sin  V max 1 cycle (360°)

Elements of a Sine Wave Alternating voltage and current vary continuously in magnitude and reverse in polarity. One complete set of values is one cycle of the ac waveform. One cycle includes 360° in angular measure or 2  rad in radian measure.

Amplitude 0 Angular Measure 0 °90 °180 °270 °360 ° 2  rad  rad  /2 rad 0 rad 3  /2 rad

Sine Wave Amplitudes The rms value is  peak value. The peak amplitude is  rms value. The peak-to-peak value is  rms value. The average value is  peak value.

Sine Wave Amplitudes (Two cycles shown) Amplitude 0  720°360° V rms V rms = x V p V av V av = x V p V p-p VpVp V p-p = 2 x V p

The default amplitude measurement is V rms. 120 V  V rms is the effective value. The heating effect of these two sources is identical. Same power dissipation

Amplitude 0 The average value is zero for the entire cycle V - 10 V V av = V The neg. alternation V av = V The pos. alternation V av = 0 V

Frequency of a Waveform  One cycle per second is 1 Hz  Audio range is 16 to 16,000 Hz  Radio-frequency range is up to 300,000 MHz (300 GHz) Frequency ( f ) is the number of cycles per second.

Sine Wave Frequency (Two cycles shown) Amplitude 0 Time 1 sec f = 2 Hz 0.5 sec

Period of a Waveform  T = 1/f  f = 1/T  The higher the frequency, the shorter the period. Period (T) is the time per cycle.

Amplitude 0 Time Period (T) s f = 1/T = 1/.0167 = 60 Hz T

Wavelength of a Waveform = v/f, where: = wavelength v = velocity of wave (such as sound or light) f = frequency  The higher the frequency the lower the wavelength.  The velocity of a radio wave is 3 x 10 8 meters/s. Wavelength ( is the distance a wave travels in one cycle.

Wavelength = v/f = 3 x 10 8 /27 MHz = 11.1 meters 27 MHz Radio Transmitter

Phase of a Waveform  Two waveforms that have peaks and zeros at the same time are in phase and have a phase angle of 0°.  When one sine wave is at its peak while another is at zero, the two are 90° out of phase.  When one sine wave has just the opposite phase of another, they are 180° out of phase. Phase angle (  is the angular difference between the same points on two different waveforms of the same frequency.

Phase Amplitude 0  The waveforms are in phase.

Phase Amplitude 0  The waveforms are not in phase.

Phase Amplitude 0  The waveforms are not in phase.

Phasor Representation Similar to vectors, phasors indicate the amplitude and phase angle of ac voltage or current. The length of the phasor represents the amplitude of the waveform. The angle represents the phase angle of the waveform.

Phasor Representation Amplitude 0 

Phasor Representation Amplitude 0 

Common AC Waveforms Sine wave * nonsinusoidal waveforms. Square wave * Sawtooth wave * Pulse wave *

Additional Notes House wiring uses 3-wire, single-phase power. The frequency of house wiring is 60 Hz.* The voltages for house wiring are 120 V to ground, and 240 V across the two high sides. Three-phase ac power has three legs that are 120° out of phase. *Many places outside N. America use a 50 Hz standard for house wiring.

N S Three Loops Rotating in a Magnetic Field N S V instantaneous (3 values)