Alternating voltage varies continuously in magnitude and periodically reverses in polarity. When alternating voltage is applied across a load resistance, the result is alternating current in the circuit.
A complete set of values repeated periodically is one cycle of the ac waveform. The cycle can be measured from any one point on the wave to the next successive point having the same value and varying in the same direction. One cycle includes 360° in angular measure, or 2 π rad.
The rms value of a sine wave is 0.707 x peak value. The peak amplitude, at 90° and 270° in the cycle, is 1.414 x rms value.
The peak-to-peak value is double the peak amplitude, or 2.828 x rms for a symmetrical ac waveform.
The average value is 0.637 x peak value.
The frequency equals the number of cycles per second. One cps is 1 Hz. The audio-frequency (af) range is 16 to 16,000 Hz. Higher frequencies up to 300,000 MHz are radio frequencies.
The amount of time for one cycle is the period T. The period and frequency are reciprocals: T = 1/f, or f = 1/T. The higher the frequency, the shorter the period.
Wavelength Λ is the distance a wave travels in one cycle. The higher the frequency, the shorter the wavelength. The wavelength also depends on the velocity at which the wave travels: Λ = v/f, where v is velocity of the wave and f is the frequency.
Phase angle is the angular difference in time between corresponding values in the cycles for two waveforms of the same frequency.
When one sine wave has its maximum value while the other is at zero, the two waves are 90° out of phase. Two waveforms with a zero phase angle between them are in phase; a 180° phase angle means opposite phase.
The length of a phasor arrow indicates amplitude, and the angle corresponds to the phase. A leading phase is shown by counterclockwise angles.
Sine-wave alternating voltage V applied across a load resistance R produces alternating current I in the circuit. The current has the same waveform, frequency, and phase as the applied voltage because of the resistive load. The amount of I = V/R.
The sawtooth wave and square wave are two common examples of nonsinusoidal waveforms. The amplitudes of these waves are usually measured in peak-to-peak value.
Harmonic frequencies are exact multiples of the fundamental frequency.
The ac voltage used in residences range from 115 to 125 V rms with a frequency of 60 Hz. The nominal voltage is usually given as 120 V.
For residential wiring, the three-wire single-phase Edison system shown in Fig. 15–21 is used to provide either 120 or 240 V.
In a motor, the rotating armature connects to the power line. The stator field coils provide the magnetic flux cut by the armature as it is forced to rotate. A generator has the opposite effect: it converts mechanical energy into electrical output.
A dc motor has commutator segments contacted by graphite brushes for the external connections to the power source. An ac induction motor does not have brushes.
In three-phase power, each phase angle is 120°. For the Y connections in Fig. 15–26a, each pair of output terminals has an output of 120 x 1.73 = 208 V. This voltage is known as the line-to-line voltage.
