AC Voltage and Current 24 July 2005Professor Andrew H. Andersen 1ELEC 103AC Voltage and Current24 July 2005 AC Voltage and Current 2Objectives• Identify a sinusoidal waveform and identify its characteristics• Describe how sine waves are generated• Determine the various voltage and current values of sine waves• Describe phase relationships of sine waves• Mathematically analyze a sinusoidal waveformAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 224 July 2005 AC Voltage and Current 3AC Alternator24 July 2005 AC Voltage and Current 4AC AlternatorAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 324 July 2005 AC Voltage and Current 5AC 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 induced24 July 2005 AC Voltage and Current 6Generation of AC VoltageAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 424 July 2005 AC Voltage and Current 7Frequency of AC24 July 2005 AC Voltage and Current 8Multi-pole ac Generator• By increasing the number of poles, the number of cycles per revolution can be increasedAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 524 July 2005 AC Voltage and Current 9Electronic 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 generator24 July 2005 AC Voltage and Current 10AC Waveform• The sine wave is a common type of alternating current (ac) and alternating voltageAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 624 July 2005 AC Voltage and Current 11Peak 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 IP24 July 2005 AC Voltage and Current 12Peak-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 peakThe peak-to-peak values are represented as:VPP and IPPwhere: VPP = 2VP and IPP = 2IPAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 724 July 2005 AC Voltage and Current 13Instantaneous 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 valuesInstantaneous values are represented as:v and i24 July 2005 AC Voltage and Current 14Instantaneous AC Voltage and CurrentAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 824 July 2005 AC Voltage and Current 15Instantaneous Voltage and Current Relationship between loop position rotating through a magnetic field and the instantaneous voltage vi at the slip ringsvi = VM sin 2πft24 July 2005 AC Voltage and Current 17Frequency 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: 1 1 f = Hz = T sAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 924 July 2005 AC Voltage and Current 18Period 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 1 1 1 1 T = s = f = Hz = f Hz T s 24 July 2005 AC Voltage and Current 19Relationship between Period and FrequencyT = 4s 1 f = = .25Hz 4s T = 1 s 1 f = = 1MHz 1s µµAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 1024 July 2005 AC Voltage and Current 20RMS 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 meterVrms = Veff = 0.707VPIrms = Ieff = 0.707IP24 July 2005 AC Voltage and Current 21Average 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 axisVavg = 0.637VPIavg = 0.637IPAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 1124 July 2005 AC Voltage and Current 22AC Voltage Measurements24 July 2005 AC Voltage and Current 23Sine Wave Relationship to Rotational MotionAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 1224 July 2005 AC Voltage and Current 24Relationship between Degrees and 1 Radian24 July 2005 AC Voltage and Current 25Relationship between Degrees and RadiansAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 1324 July 2005 AC Voltage and Current 26Relationship between Degrees and Radians24 July 2005 AC Voltage and Current 27Phase Shift Between Two WaveformsOnly meaningful between two waveforms of the same frequencySelect one waveform as the reference (waveform A above) and measure between two common pointsAC Voltage and Current 24 July 2005Professor Andrew H. Andersen 1424 July 2005 AC Voltage and Current 28Phase Shift Between Two