ac voltage and current.pptx

7/24/2019 AC Voltage and Current.pptx

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Alternating Voltages

and Currents


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Introduction

Electricity is produced by generators at powerstations and then distributed by a vast network oftransmission lines (called the National Grid systemto industry and for domestic use!

It is easier and cheaper to generate alternatingcurrent (a!c! than direct current (d!c! and a!c! ismore conveniently distributed than d!c! since its

voltage can be readily altered using transformers!

"hen# ever d!c! is needed in preference to a!c!$devices called recti%ers are used for conversion!


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Introduction

&et a single turn coil be free to rotate at constantangular velocity symmetrically between the poles ofa magnet system as shown in 'igure )!!


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IntroductionAn e!m!f! is generated in the coil (from 'araday*s

&aws which varies in magnitude and reverses itsdirection at regular intervals! +he reason for this isshown in 'igure )!,! In positions (a$ (e and (i theconductors of the loop are e-ectively moving alongthe magnetic %eld$ no .u/ is cut and hence no

e!m!f! is induced!


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Introduction

In position (c ma/imum .u/ is cut and hencema/i# mum e!m!f! is induced! In position (g$ma/imum .u/ is cut and hence ma/imum e!m!f! isagain induced!


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Introduction

0owever$ using 'leming*s right#hand rule$ theinduced e!m!f! is in the opposite direction to that inposition (c and is thus shown as 1 E.


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Introduction

In positions (b), (d), (f) and (h) some ux is cutand hence some e.m.f. is induced. If all suchpositions of the coil are considered, in onerevolution of the coil, one cycle of alternating e.m.f.is produced as shown. This is the principle of

operation of the a.c. generator (i.e. the alternator).


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"aveforms

If values of 2uantities which vary with time t are

plotted to a base of time, the resulting graph iscalled a waveform. ome typical waveforms areshown in !igure "#.$. %aveforms (a) and (b) areunidirectional waveforms, for, although they varyconsiderably with time, they ow in one directiononly (i.e. they do not cross the time axis andbecome negative) and negative).


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"aveforms%aveforms (c) to (g) are called alternating

waveforms since their &uantities are continually

changing in direction (i.e. alternately positive andnegative).


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"aveformsA waveform of the type shown in 'igure )!3(g

is called a sine wave! It is the shape of the

waveform of e!m!f! produced by an alternator andthus the mains electricity supply is of 4sinusoidal*form!


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"aveforms5ne complete series of values is called a cycle

(i!e! from ' to in !igure "#.$(g)).

The time taen for an alternating &uantity tocomplete one cycle is called the period or the

periodic time, T, of the waveform.


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"aveformsThe number of cycles completed in one second

is called the fre&uency, f, of the supply and is

measured in hert*, +*. The standard fre&uency ofthe electricity supply in reat -ritain is / +*.

T 0 "1f or f 0 "1T


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"aveforms

Problem 1.

Determine the periodic time for frequenciesof (a) 50 Hz and (b) 20 kHz.

a 6eriodic time +78f 7 89: 7 :!:,s or ,:ms

(b 6eriodic time + 7 8f 7 8,:::: 7 :!::::9s or

9: ;s


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"aveforms

Problem #.

$n alternatin% current completes 5 c&cles in 'ms. hat is its frequenc&

+ime for cycle 7


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A!C! Values

Instantaneous values are the values of thealternating 2uantities at any instant of time!

+hey are represented by small letters$ i$ >$ e$etc! (see 'igures )!3(f and (g!


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A!C! Values+he largest value reached in a half cycle is

called the peak value or the ma/imum value or theamplitude of the waveform! ?uch values arerepresented by Vm $ Im $ etc! (see 'igures )!3(fand (g! A peak#to#peak value of e!m!f! is shown in

'igure )!3(g and is the di-erence between thema/imum and minimum values in a cycle!


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A!C! Values+he average or mean value of a symmetrical

alternating 2uantity$ (such as a sine wave$ is theaverage value measured over a half cycle$ (sinceover a complete cycle the average value is @ero!Average or mean value 7 area under the curve

length of base


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A!C! Values+he area under the curve is found by

appro/imate methods such as the trape@oidal rule$the mid#ordinate rule or ?impson*s rule! Averagevalues are represented by 565, I65, etc.

For a sine wave, average value = 0.637 maximum valuei.e. 2!" maximum value#


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A!C! Values

+he e-ective value of an alternating current isthat current which will produce the same heatinge-ect as an e2uivalent direct current!

+he e-ective value is called the root means2uare (r!m!s! value and whenever an alternating2uantity is given$ it is assumed to be the r!m!s!value!


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A!C! Values'or e/ample$ the domestic mains supply in

Great ritain is ,): V and is assumed to mean ,):V r!m!s!

+he symbols used for r!m!s! values are I , 5 , E ,etc. !or a non7sinusoidal waveform as shown in

!igure "#.# the r.m.s. value is given by8


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A!C! Values

+he values of form and peak factors give an

indication of the shape of waveforms!


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A!C! Values6roblem )!

'or the periodic waveforms shown in 'igure)!9 determine for eachB (i fre2uency (ii averagevalue over half a cycle (iii r!m!s! value (iv formfactor and (v peak factor!


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A!C! Values(a+riangular waveform ('igure )!9(a

(i +ime for complete cycle 7 ,:ms 7 periodictime$ T.+ence fre&uency f 0 "1T 0 "19/2"/3$0 50Hz


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A!C! Values


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A!C! Values


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A!C! Values


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A!C! Values


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A!C! Values


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A!C! Values


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A!C! Values

Assuming the negativehalf cycle is identical inshape to the positive halfcycle$ plot the waveform and%nd (a the fre2uency of thesupply$ (b the instantaneousvalues of current after !,9ms and 3!< ms$ (c the peak

or ma/imum value$ (d themean or average value$ and(e the r!m!s! value of thewaveform!


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A!C! Values


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A!C! Values


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*lectrical +afet& , -nsulationand uses

-nsulationis used to prevent 4leakage*$ and whendeter# mining what type of insulation should be used$the ma/imum voltage present must be taken intoaccount! 'or this reason$ peak values are always

considered when choosing insulation materials!

usesare the weak link in a circuit and are used tobreak the circuit if e/cessive current is drawn!

E/cessive current could lead to a %re! 'uses rely onthe heating e-ect of the current$ and for this reason$r.m.s /alues must ala&s be used hencalculatin% the appropriate fuse size.

ac voltage and current.pptx

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