Principles & Applications Electricity Principles & Applications Sixth Edition Richard J. Fowler Chapter 8 Alternating Current and Voltage ©2003 Glencoe/McGraw-Hill

INTRODUCTION Types of Waveforms Induced Voltage Generating a Sine Wave Ac Terminology Three-Phase Ac

Electrical Waveforms Alternating current or voltage Pulsating direct current or voltage Fluctuating direct current or voltage

-1 -2 Ac Waveform Terminology 1st cycle 2nd cycle 3rd cycle +2 +1 -1 -2 Voltage or Current peak to + peak - peak 0.2 s 0.4 s 0.6 s Time T = period = time to complete 1 cycle = 0.2 s f = frequency = 1 / T = 1 / 0.2 s = 5 Hz Peak amplitude can be either negative or positive. Peak-to-peak amplitude includes both the - and + peaks.

Specifying Sine-Wave Amplitude peak peak-to-peak rms = 0.707 peak av = 0.637 peak peak = (1 / 0.707) rms = 1.414 rms peak = (1 / 0.637) av = 1.57 av peak = peak-to-peak / 2 Examples: 20 Vp-p / 2 = 10 Vp and 10 Vp x 0.707 = 7.07 V 8 Aav x 1.57 = 12.56 Ap

Wave-Form Quiz The ____ dc waveform never reaches or crosses the zero reference line. fluctuating The part of the waveform that includes its complete negative and positive excursions is called a ____. cycle The ____ is the time required to complete one cycle. period The base unit of frequency is the ____. hertz For a sine wave, 30 VP = ____ V. 21.21 For a sine wave, 10 AP-P = ____ A. 3.535 For a sine wave, 25 V = ____ VP. 35.35

Constant-speed Conductor Induced Voltage in a Constant-speed Conductor N S N S N S N S If motion is parallel to the flux, When motion is at an angle, When motion is perpendicular to the flux, Reversing the direction of motion, no flux is cut; some flux is cut; thus no voltage is induced. and some voltage is induced. reverses the polarity of the induced voltage. maximum voltage is induced.

Generating a Sine Wave S N Motion is parallel to the flux. No voltage is induced.

Induced voltage is 0.707 of maximum. Generating a Sine Wave S x N Motion is 45° to flux. Induced voltage is 0.707 of maximum.

Generating a Sine Wave S N Motion is perpendicular to flux. Induced voltage is maximum.

Generating a Sine Wave S N Motion is 45° to flux. Induced voltage is 0.707 of maximum.

Generating a Sine Wave S N Motion is parallel to flux. No voltage is induced.

Generating a Sine Wave S N Motion is 45° to flux. Notice current in the conductor has reversed. Induced voltage is 0.707 of maximum.

Generating a Sine Wave S N Motion is perpendicular to flux. Induced voltage is maximum.

Generating a Sine Wave S N Motion is 45° to flux. Induced voltage is 0.707 of maximum.

Generating a Sine Wave S N Motion is parallel to flux. No voltage is induced. Ready to produce another cycle.

Ac Generation Quiz Maximum voltage is produced when a perpendicular conductor is moving ____ to the flux. perpendicular No voltage is produced when a conductor is moving ____ to the flux. parallel When a conductor is moving at 45° to the flux, the voltage is ____ of maximum value. 0.707 For a two-pole generator, one cycle of ac is produced during ____ revolution(s). one To produce a sine wave the flux field must be ____. uniform

Three-Phase Waveform Phase 1 Phase 2 Phase 3 120° 120° 120° 240° Phase 2 lags phase 1 by 120°. Phase 3 lags phase 1 by 240°. Phase 2 leads phase 3 by 120°. Phase 1 lags phase 3 by 120°.

Generation of Three-Phase Ac x S Phase 1 Phase 2 Phase 3 The algebraic sum of the instantaneous voltages of the three phases equals zero. Phase 1 is ready to go positive. Phase 2 is going more negative. Phase 3 is going less positive.

Delta Connections Delta-Connected Load Delta-Connected Source Line 1 Phase 3 Phase 2 Phase 1 Line 2 Line 3 Delta-Connected Load Delta-Connected Source Each load resistor will be connected to one of the phases. The sum of the instantaneous phase voltages equals zero. For the delta-to-delta connection, Vline = Vphase = Vload. For the delta-to-delta connection, Iline = 1.732 Iphase = 1.732 Iload.

Wye Connections Wye-Connected Source Wye-Connected Load Line 2 Line 1 Phase 3 Phase 1 Phase 2 Line 3 Wye-Connected Source Wye-Connected Load For the wye-to-wye connection with a balanced load: I line = Iphase = Iload. Vline = 1.732 Vphase = 1.732 Vload. There is no voltage between the source and load star points.

Three-Phase Ac Quiz In a three-phase system, the phases are separated by ____ electrical degrees. 120 In a three-phase system, the phase coils are separated by ____ mechanical degrees. 120 The algebraic sum of the instantaneous phase voltages equals ____. zero The phase coils in a ____ connected source are connected in series. delta- Phase and line currents are equal in a ____ connected system with balanced loads. wye- In a delta-connected system, the line current equals ____ times the phase current. 1.732

REVIEW Induced Voltage Generating a Sine Wave Ac Terminology Types of Waveforms Induced Voltage Generating a Sine Wave Ac Terminology Three-Phase Ac