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Average Value and RMS Value : Problem 1 - AC Circuits - Basic Electrical Engineering - YouTube
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- hi friends in this video we are going
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to see how to calculate average and RMS
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value of AC quantity
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so here I have taken a waveform which is
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changing like this or a triangular
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manner but it is a AC waveform because
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it is changing its magnitude with
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respect to time so for this waveform we
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are supposed to calculate average value
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and RMS value we will use analytical
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method now two things we have to
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remember one tracing the cycle and
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second writing equation of a waveform so
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this particular waveform having this
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cycle which will repeat itself so once
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we decided a cycle we can get a time
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period of that waveform so cycle exists
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from 0 to 1 so time period is nothing
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but capital T equal to 1 second because
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cycle exists for this much of time
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secondly we have to write an equation of
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wave form during a time period so it is
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a simple straight line given like this
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so coordinates of these two points is 0
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comma 0 and for this point it is 1 comma
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10 so I can use equation of a straight
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line
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it says y 2 minus y 1 upon X 2 minus X 1
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equal to Y 1 minus y divided by X 1
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minus X so here I will consider this as
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x1 y1 x2 y2 and x-axis is T y-axis is I
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of T so if I substitute what I will get
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Y 2 is 10 y 1 is 0 divided by X 2 X 2 is
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1 X 1 is 0 equal to Y 1 so Y 1 is 0
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again minus Y is I of t upon X 1 H 1 is
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0 again minus X x axis is time axis is T so
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if I simplify what I will get n upon 1
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equal to minus I of T upon minus T so if
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I solve I will get I of T equal to 10
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times T so finally what I get for this
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waveform is equation I of T equal to 10
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T for T greater than 0 and less than 1
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so what I have done I have decided what
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is a time period secondly I have got
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equation of the wave form
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now the problem will become very easy
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because we know average value equal to 1
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upon time period we have to integrate
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that particular waveform for the time
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period t so in this case what I will get
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1 upon 1 and I am having a waveform only
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from 0 to 1 so 0 to 1 and equation of
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this I is 10 T so our average equals 10
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I will take out of a integration
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integration of T is T Square by 2 and
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lets apply the limits lower limit is 0
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upper limit is 1 so if I solve I will
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get average value as 10 divided by 2 in
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bracket 1 square minus 0 square so
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ultimately it is 5 only so it is a 5
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ampere so average value I am getting 5
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ampere same way I can get RMS value so
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to get an RMS value the formula is I RMS
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equals root of 1 by T integration over a
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time period t but this time it is the
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integration of I square so lets
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substitute the value 1 upon 1 waveform
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exist from 0 to 1 I is 10 T so 10 T
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Square into DT
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so it is route integral 0 to 1 100
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t-square 100 is a constant I will take
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it out of integration so finally I will
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get integral 0 to 1 T Square DT and we
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know integration of T Square is T cube
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divided by 3 and limits are 0 and 1 so
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if I apply the limits what I will get I
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RMS equal to root 100 divided by 3 1
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cube minus 0 cube so ultimately it is
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root 100 divided by 3 and if I solve
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what I will get I RMS as 5.7733
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ampere so what
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I have done over here a simple
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triangular wave I am consider and
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Illustrated how to calculate average and
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RMS value by considering two thing one
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we have to define what is the cycle and
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second in the cycle how the time period
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is changing as per that we have to write
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equation of wave form thank you
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