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AC Signals Sinusoidal Signal An ideal generator produces 1 period = T an induced emf that oscillates. 0 • Sine or cosine wave t The oscillation is characterized by its period. 2t 0 cos T 0 cos 2ft 0 cos t The inverse of the period is the frequency. • f = 1/T • Cycles per sec, or Hz • Angular frequency in radians Amplitude The amplitude of a sinusoidal signal is the peak value. • Also maximum negative value The average value is zero. • equally above and below zero 0 t -0 The average value of the square is half the peak squared. 02 • Root mean square value rms 02 2 0 2 0 t Phase The phase of a signal f = t/T compares the time at a point to the time for the peak. 0 • Fraction of a period t Phase is measured as an angle. 2t f T t f 360 T • Divided into 2 radians • Compare to 360° Phasor A phasor diagram maps the cosine onto the x-axis of a circle. • x = cos t A vector represents a changing value like voltage. • Magnitude for amplitude • Angle for phase • Moves counterclockwise with time q cos q AC Resistance An AC source and resistor make a one-loop circuit. v R The resistor voltage must vR V0 cos t i i V0 cos t R V0 cos 2ft R balance the source voltage. • Lower case for AC The current follows from Ohm’s law. • Oscillates as well Power Loss Power loss in an AC circuit depends on the instantaneous voltage and current. v2 p vi i 2 R R P 2 I0 R 0 t Average Power It’s more useful to look at the 2 Prms I rms R average power loss. • Use RMS voltage or current. The form can reflect current, 2 Vrms R voltage or both. Prms P Prms Vrms I rms 2 I0 R Prms 0 t next