AC Voltage and Current
12 February 2004
AC Voltage and Current
Objectives
• Identify a sinusoidal waveform and measure its characteristics
• Describe how sine waves are generated
• Determine the various voltage and current values of sine
waves
• Describe angular relationships of sine waves
• Mathematically analyze a sinusoidal waveform
• Apply the basic circuit laws to ac resistive circuits
• Determine total voltages that have both ac and dc components
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AC Waveform
• The sine wave is a common type of alternating current (ac) and
alternating voltage
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AC Generator
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AC Alternator
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AC Alternator
• The ac generator has slip rings
that pick up the induced
voltage through a complete
rotation cycle
• The induced voltage is related
to the number of lines of flux
being cut.
• When the loop is moving
parallel with the lines of flux,
no voltage is induced.
• When the loop is moving
perpendicular to the lines of
flux, the maximum voltage is
induced
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Generation of AC Voltage
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Frequency of AC
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Multi-pole ac Generator
• By increasing the number of poles, the number of cycles per revolution can
be increased
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Electronic Signal Generators
• In the lab, we usually use a signal generator to produce a
variety of waveforms at a wide range of frequencies
– An oscillator in the signal generator produces the repetitive wave
– We are able to set the frequency and amplitude of the signal from the
signal generator
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Instantaneous Values of Sine Waves
• The instantaneous values of a sine wave voltage (or current)
are different at different points along the curve, having
negative and positive values
Instantaneous values are represented as:
v and i
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Instantaneous AC Voltage and Current
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Peak Voltage of a Sine Wave
• The peak value of a sine wave is the value of voltage or
current at the positive or negative maximum with respect to
zero
• Peak values are represented as:
VP and IP
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Peak-to-Peak Value of a Sine Wave
• The peak-to-peak value of a sine wave is the voltage or
current from the positive peak to the negative peak
The peak-to-peak values are represented as:
VPP and IPP
where: VPP = 2 VP and IPP = 2 IP
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Frequency of a Waveform
• Frequency ( f ) is the number of complete cycles that a sine
wave completes in one second
– The more cycles completed in one second, the higher the frequency
– Frequency is measured in hertz (Hz)
• Relationship between frequency ( f ) and period (T) is:
f=
1
T
1
s
Hz =
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Period of a Waveform
• The time required for a sine wave to complete one full cycle is called the
period (T)
– A cycle consists of one complete positive, and one complete negative
alternation
– The period of a sine wave can be measured between any two corresponding
points on the waveform
T=
1
f
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s=
1
Hz
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Relationship between Period and Frequency
T = 4s
1
f=
= .25Hz
4s
T = 1µs
f=
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1
= 1MHz
1µs
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RMS Value of a Sine Wave
• The rms (root mean square) value, or effective value, of a sinusoidal
voltage is equal to the dc voltage that produces the same amount of heat in
a resistance as does the sinusoidal voltage
• RMS is the voltage measured with meter
Vrms = Veff = 0.707VP
Irms = Ieff = 0.707IP
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Average Value of a Sine Wave
• The average value is the total area under the half-cycle curve
divided by the distance in radians of the curve along the
horizontal axis
Vavg = 0.637VP
Iavg = 0.637IP
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Sine Wave Relationship to Rotational Motion
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Relationship between Degrees and 1 Radian
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Relationship between Degrees and Radians
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Relationship between Degrees and Radians
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Instantaneous Voltage and Current
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Phase Shift Between Two Waveforms
Only meaningful between two waveforms of the same
frequency
Select one waveform as the reference (waveform A above)
and measure between two common points
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Phase Shift Between Two Waveforms
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Ohm’s Law
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Nonsinusoidal Waveforms - Pulse
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Nonsinusoidal Waveforms - Ramp
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Nonsinusoidal Waveforms - Triangular
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Nonsinusoidal Waveforms - Sawtooth
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