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Effective Value of RMS - AC Circuits - Basic Electrical Engineering - YouTube
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hi friends in this video we are going to
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see the most important parameter of AC
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voltage waveform and that is RMS or
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effective value lets see the
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definition of it the effective or RMS
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value of an alternating quantity is
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given by that steady current which when
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flowing through a given circuit for a
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given time produces the same amount of
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heat as produced by the alternating
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current which when flowing through the
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same circuit for the same time meaning
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suppose I perform my experiment where I
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connect a DC supply to a lamp and I will
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measure a power by passing a DC current
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for some amount of time now instead of a
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DC I will replace AC and I will check
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the same effect for same amount of time
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the moment I will get a same effect
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that value of AC I noted down which is
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nothing but RMS value so in short I can
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say RMS value of AC quantity is nothing
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but its DC equivalent meaning if I
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replace the RMS value of AC with the
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same amount of DC I will get same effect
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so lets move to the next point the
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next point is I will elaborate the same
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concept with example so what I have over
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here I have a AC supply given by the
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socket and I will measure the effect
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suppose it is giving a 240 volt AC 240
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volt AC is doing the same amount of work
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as if 240 volt DC so this particular
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example will clear the idea of RMS so
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what is the advantage of RMS value
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everywhere AC is denoted by its RMS
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value because RMS value of AC is nothing
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but a useful component of AC voltage or
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AC current which is responsible
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for production of actual power or
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responsible for doing a work done so
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everywhere whenever we see a voltage
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that is always a rms value just take an
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example whenever we have a domestic
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household supply that is single-phase
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230 volt AC 50 Hertz so this 230 volt is
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nothing but RMS value of AC supply now
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effective value can be calculated by two
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ways one is a graphical and second is a
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analytical way so let us say a graphical
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method so in graphical method I have
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considered only a half cycle right so
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its RMS is nothing but a root mean
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square so what we have to do we have to
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take a mean of square of every
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instantaneous values and then we have to
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take the square root of it so what I
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have done only half wave I have
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considered only half cycle I have consider
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so same effect can be true for a full
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cycle so in half cycle I have considered
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this 12 instance so this 12 instance
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says giving you to an instantaneous
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values of voltages v1 v2 v3 like that so
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as per the definition it is a root of
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mean of square of instantaneous values
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so that will give you VRMS equal to
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root of V1 square plus V2 square plus
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V3 square like that till with 12 square
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divided by 12 because I have considered
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12 values in general if I have n number
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of values I will get RMS voltage at V
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RMS equal to root of V1 square plus V2
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square like that till VN square divided
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by n for a current if I replace V by I
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I will get I RMS as root of I1 square
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plus I2 square plus I2 square up to In
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square divided by N
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so in a graphical way what we do a
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waveform be splitted into number of
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instances and for every instant we get
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the instantaneous value square it
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likewise we take addition of all the
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squaring of all the instantaneous values
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divided by number of instances we are
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considered and then ultimately we take a
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root we will get a rms value by a
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graphical method suppose I want to find
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out rms value by another technique which
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is analytical method see how we are
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going to do that so the current is given
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by I equal to IM sine theta a standard
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AC current waveform then let's square it
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so I get I square equal to IM square
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sine square theta so in now this figure
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I have shown the Im sine theta like
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this and squaring of it will be like
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this so what we are doing we are
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considering the area under this curve
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which is nothing but a integral 0 to pi I
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Square D theta and length of this is
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nothing but pi because we are just
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considering half cycle so if I solve
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further what I will get average value of
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square of the current over half cycle is
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given by area of curve over half cycle
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divided by length of curve for half
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cycle so it gives me integral 0 to pi I
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Square D theta divided by length is PI
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so that is ultimately 1 over PI I can
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take it out 0 to PI I Square D theta
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then 1 upon PI 0 to PI is a limits for
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integral I we know its IM sine theta
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and squaring is IM square sine square
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theta D theta we know sine square theta
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is given by 1 minus cos 2 theta divided
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by 2 so I have replaced that constant I
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will take out of integration so I will
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get this expression IM square divided
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by PI integral exist from 0 to PI
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I 1 minus cos 2 theta divided by 2 into
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D theta integral of 1 is theta if I take
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a 1 by 2 common so ultimately I will get
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1 minus cos 2 theta inside an integral
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integral of 1 is Theta integral of cos 2
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theta is sine 2 theta divided by 2 if I
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apply the limits ultimately I will get IM
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square divided by 2 but that is
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nothing but a average value of square
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of the current what we want root mean
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square so RMS value of current is
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nothing but the root of this value so I
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RMS equal to root of
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IM square divided by 2 if I further
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simplify I will get IRMS as IM
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divided by root 2 so in a voltage case I
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will get VRMS as VM by root 2 and we
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know 1 by root 2 as 0.707 so finally I
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can say IRMS is 0.707
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IM VRMS equal to 0.707
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VM RMS is very important
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parameter for AC because all the meters
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voltage are volt meter for a voltage
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measurement emitter for current
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measurement are designed in RMS values
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and whenever I see any AC voltage or any
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AC current I am talking about RMS
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voltage or RMS current only thank you
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