Average Value of AC Voltage - AC Circuits - Basic Electrical Engineering - YouTube

hi friends in this video we are going to

see one more important parameter of AC

voltage waveform and that is average

value lets see the definition of average

value the average value of an

alternating quantity is defined as that

value which is obtained by averaging all

the instantaneous values over a period

of half cycle now one half cycle is

required for calculation of average

value because AC waveform we have seen

that it is a sinusoidal in nature it has

two positive as well as a negative off

cycles which are identical one so thing

is that if I average or if I add all the

instantaneous values in positive as well

as negative off cycle

ultimately it sums up towards 0 so

you can say average value is 0 but

that is not a case whenever we calculate

average value of a such waveform we need

to take only half cycle because it is

understood remaining half is identical

to the first half only sine is changing

so in order to avoid this problem we

always take half cycle while calculation

of average value so every value can be

calculated by two way one is a graphical

and second is analytical so what

graphical method is I am considering a

half cycle and in this half cycle I

have consider so many instances so let

us look at 12 instances I have

calculated and for every instant I

calculate the instantaneous value of a

current or a voltage and simply I will

add them and divided by number of

instances we are taken so that gives

rise to this formula for 12

instances I have V average as v1 plus v2

plus v3 up to Whitwell divided by 12 in

general suppose I am having n number of

points so I will get V average as v1

plus v2 plus v3

up to VN / n same way instead of a

voltage if I want to get average current

it is given by I average equal to i1

plus i2 plus i3 up to In divided by n

so this is a one way of a calculation of

average value let us go to the second

way and that is analytical method so

what do we do in an analytical method we

just consider the area covered by this

half cycle so what I will consider a

small element I will consider and then I

integrate over a half cycle I will get a

average value so lets solve so the

average value can be obtained by taking

the ratio of area under the curve or a

half cycle to length of base of half

cycle so I average is equal to area under curve

for half cycle and we have seen that it

is integral 0 to PI I dtheta because

I D theta is that small element which we

need to integrate to complete area

of the half cycle and length of half

cycle is PI so 1 over PI I can take it

out integral 0 to PI by ID theta if I

solve instead of I I need to substitute

IM sine theta I am I can take it out

as it is constant so IM by PI integral

0 to PI sine theta D theta sine theta

integral a is the minus cos theta and if

I apply the limits I will get value 2IM 75 00:03:50,090 --> 00:03:58,130 by PI 2 by PI is a constant and if we

solve you will get that constant number

0.637 so I can say I average

is nothing but 0.637 IM

similarly V average I can say 0.637

VM so every value is nothing but

63.7% of the maximum value for AC

quantity what is the advantage of this

average value we have seen that

whenever required this AC can be

converted into a DC so whenever we are

converting this AC into DC what value

exactly we can pass while applying a DC

supply and that is given by this average

value so average value is nothing but

whenever I convert AC into DC and

without any filteration if I check the

voltage that voltage is nothing but

average value thank you