AC Signals

Sinusoidal Signal  An ideal generator produces an induced emf that oscillates. Sine or cosine wave  The oscillation is characterized by its period.  The inverse of the period is the frequency. f = 1/T Cycles per sec, or Hz Angular frequency in radians 1 period =  t 00

Amplitude  The amplitude of a sinusoidal signal is the peak value. Also maximum negative valueAlso maximum negative value  The average value is zero. equally above and below zeroequally above and below zero  The average value of the square is half the peak squared. Root mean square valueRoot mean square value t 00  0 t 0202 0

Phase  The phase of a signal compares the time at a point to the time for the peak. Fraction of a period  Phase is measured as an angle. Divided into 2  radians Compare to 360°  = t/  t 00

Phasor  A phasor diagram maps the cosine onto the x-axis of a circle. x =  cos  tx =  cos  t  A vector represents a changing value like voltage. Magnitude for amplitudeMagnitude for amplitude Angle for phaseAngle for phase Moves counterclockwise with timeMoves counterclockwise with time    cos 

AC Resistance  An AC source and resistor make a one-loop circuit.  The resistor voltage must balance the source voltage. Lower case for AC  The current follows from Ohm’s law. Oscillates as well R v

Power Loss  Power loss in an AC circuit depends on the instantaneous voltage and current. t0 P

Average Power  It’s more useful to look at the average power loss. Use RMS voltage or current.Use RMS voltage or current.  The form can reflect current, voltage or both. next t0 P