Alternating Current Circuit

PART1:ALTERNATINGCURRENTS

AlternatingCurrentSignals
MostoftheenergysourceweuseinourelectricorelectronicdevicesisfromACsource.This is sometimes converted into DC source.
Thetermalternatingindicatesonlythatthewaveformalternatesbetweentwoprescribed levels in a set time sequence.
Alternating current (AC) theory is concerned with the mathematical analysis of thesteady statebehaviorofelectrical circuits in which the currents and voltages varyperiodically
withtime.

Alternatingcurrentisproducedinacircuitwhenthepotentialdifference(whichwecall
voltage)betweentheterminalsoftheseatofemfinthecircuitchangessignfrommoment

tomoment.ThemostcommonsuchseatofemfiscalledanACgenerator.

ThevoltageVbetweenitsterminalsofanACgeneratorisgivenby

V V ft = π 0sin 21 where V0is the magnitude of the maximum voltage (the voltage amplitude), f is thefrequency (in cycles per second) and t is the time in seconds. As we shallsee,suchavoltageisveryeasilyproducedbyarotatingarmature.SymbolforanAC generator:

ThevoltageVproducedbetweentheterminalsofanACgeneratorfluctuatessinusoidally with time.

IfanACgeneratorisplacedacrossaresistorRthecurrentinthecircuitisgivenby:
V

sin2sin2⎛⎞
()()
IftIft
=π=π⎜⎟⎝⎠
0
2
R
0

0whereisthecurrentamplitude.0=V
I
R

Whatever the source of origin, the electric current is fundamentally the same inallcases,but the manner in which it varies with time may be very different. This is shown bythegraphof the current plotted against time as a base, and a number of Examples are illustrated below.

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Figure1.1(a)to(l)showingdifferenttypesofelectriccurrents.

representsasteadydirectcurrent(D.C.)ofunvaryingmagnitude,suchasisobtained from an accumulator.
    represents a D.C. obtained from a d.c. generator, and consists of a steady D.C. superimposed on which is a uniform ripple of relatively high frequency, due to the commutator of the d.c. generator. As the armature rotates the commutator segments come under the brush in rapid succession and produce arippleinthevoltagewhichis reproduced in the current.
represents a pulsating current varying periodically between maximum and minimum limits. It may be produced by adding a D.C. to an A.C. or vice versa. The d.c. componentmustbethelargerif the current is unidirectional. All the first three types of current are unidirectional, i.e. they flow in one direction only.
representsapurealternatingcurrent(A.C).Thecurrentflowsfirstinonedirectionand then in the other in a periodic manner, the time of each alternationbeingconstant.In the ideal case the current varies with time according to a sine law, when it is said to

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be sinusoidal. Considering the time of a complete cycle of current (a positive half wave plus a negative half-wave) as equal to 360°, the instantaneous values of the currentareproportionaltothesineoftheanglemeasuredfromthezeropointwhere the current is about to rise in the positive direction.
representsatypeofA.C.withadifferentwaveform.SuchanA.C.issaidtohavea peaked wave form, the term being self-explanatory.
represents anA.C.withyetanotherdifferentwaveform.SuchanA.C.issaidtohavea flat-topped wave form, the term again being self-explanatory. Both this and the previous Example represent cases of A.C. having non-sinusoidal wave forms.
representsan Example of an oscillating current, and is similar in shape to (d) except that it has a much higher frequency. An oscillating current is usually regarded as one having a frequency determined by the constants of the circuit, whereas an alternating current has a frequency determined by the apparatus supplying the circuit.
representsanother type of oscillating current which is known as damped. The current again has a constant frequency, but its amplitude is damped, i.e. it dies down, after which it is brought back to its original value.
represents yet anothertype of oscillating current, this time known as a modulated current. The amplitude varies rhythmically between maximum and minimum values.It may even die down to zero.
The next three Examples represent various types of transient currents. These transient currents usually die away extremely rapidly, and times are generally measured in microseconds. The first Example shows a current dying away to zero, and is an Example of a unidirectional transient. Theoretically it takes an infinite time to reach absolute zero.
representsasimplea.c.transient.Thecurrentgraduallydiesdowntozeroasinthe previous case, but this time it is an A.C. that is dying away.
represents a peculiar, but not uncommon, type of a.c. transient. The current is initially unidirectional, but it gradually becomes an ordinary A.C. The positive half-waves die away much more rapidly than the negative half-waves grow, so that the finalamplitude is very much reduced.

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A.CvsD.Csources
Electricityisproducedbygeneratorsatpowerstationsandthendistributedbyavastnetwork
of transmission lines (called the National Grid system) to industry and for domestic use.∙It iseasierandcheapertogeneratealternatingcurrent(a.c.)thandirectcurrent(d.c).∙Thea.c.is more conveniently distributed than d.c. since its voltage can be readily alteredusing transformers (step-up or step-down).
Wheneverd.c.isneededinpreferencetoa.c.,devicescalledrectifiersareusedfor conversion.

A.Casawave-form
Propertiesofsinusoids
ThevoltagevproducedbetweentheterminalsofanACgeneratorfluctuatessinusoidally with time.
An AC voltage (or ac current) varies sinusoidally with time, as shown below. This is a periodicvoltagesinceitvarieswithtimesuchthatitcontinuallyrepeats.∙Period(T):The timeinterval(inseconds)betweensuccessiverepetitionsofaperiodicwaveform.Thiscan also be called the Periodic Time of the waveform for sine waves, orthe Pulse Width for square waves.
Cycle:Theportionofawaveformcontainedinoneperiodoftime.
Frequency(Hertz):isthenumberoftimesthewaveformrepeatsitselfwithinaonesecond timeperiod.Frequencyisthereciprocalofthetimeperiod,(ƒ=1/T).∙TheAmplitude(A): is the magnitude or intensity of the signal waveform measured involts or amps.
Instantaneousvalue:Themagnitude(values)ofthealternatingquantities(waveform)at any instant of time; They are represented by small letters, i, v, e etc.
Peakamplitude:Themaximumvalueofthewaveformasmeasuredfromitsaverage (or mean) value. Also referred to as maximum value orthecrestvalueortheamplitudeof
the waveform. Such values are represented by uppercase letters Vm, Im or Vo, IoorVp, Ip.