Hi friends in this video we are going to
see how to represent a voltage and
current into a phasor form and using
phasor forms how to get resultant so
this is a problem it says find the
resultant of the following that means
there are four quantities given all of
them are voltages e 1 is given as 25
sin Omega T e 2 10 sine Omega T plus PI
by 6 e 3 30 cos Omega t and e 4 20 sin
Omega t minus PI by 4 we are supposed to
find out the resultant and that will
draw all phasers so how to start one
thing you have to keep in mind all these
are the equations of a standard
sinusoidal waveform the first step we
have to compare these equations with
standard sinusoidal waveform so I am
comparing with e equal to e M sin Omega
T plus Phi make sure that all the wave
forms are equations given should have
this form sin Omega T plus Phi so if I
compare first equation I will get em 1 25
and Phi 1 is zero degree so I can say e
1 can be represented as 25 at an angle 0
volt
so what I have done from the equation
I got a phasor form similarly e 2  I can
write directly it is 10 at an angle PI
by 6 Radian lets convert that into a
degree so e 2 is nothing but 10 at an
angle 30 degree
I cannot compare e 3 directly with this
standard equation why because in
standard equation it is sin and here it
is cos so I need to convert this cos
into sin so the formula is cos theta
can be written sin 90 minus theta or
sin 90 plus theta which one we will
take how to decide whenever I use a
formula for cos to sign conversion I
have to make sure that theta should
remain positive
why because theta means Omega T over
here and this is a frequency so in a
standard equation Omega T is always
remains positive so whenever I am to
convert cosine into sin I have to make
sure that this Omega T term should
remain positive hence I will use second
formula so the e3 is given as 30 cos
Omega T which is nothing but 30 sin
Omega T plus PI by 2
so that I will get e 3 as 30 at an angle
PI by 2
Radian or e3 is 30 at an angle 90
degree volt and E 4 is given as 20 sin
Omega t minus PI by 4 simple comparison
will give me E 4 as 20 at an angle minus
pi by 4 Radian or in degree it will be
20 at an angle minus 45 degree both now
considering all these equations if I
want to get a resultant it will be very
difficult problem because every time I
have to use sin to cos Conversion
or maybe a factorization de
factorization formula instead what I
have done all the wave forms equations I
converted into phasors and this phasors
I am going to insert in calculator to
get a resultant so resultant EMF Er is
e 1 bar plus e 2 bar plus e 3 bar plus
e 4 bar bar indicates it's a vector
quantity having the magnitude along with
the angle so let us write what is e 1 so
e 1 we have calculated as 25 at an angle
0 e 2 10 at an angle 30 e 3 30 at an
angle 90 and E 4 20 at an angle minus 45
degree if I insert this value in
calculator and calculate I will get
resultant as 47.8024  plus J
20.8579 volt
its a complex quantity real part and
imaginary part but what we want we want
this in a polar form so in polar form I
will get e r as 52.1548
at an angle 23.57
degree volt once you got an
answer in phasor form it will be very
easy to write in a equation form how I
can say er is nothing but this is a
maximum value because everywhere we have
consider maximum value for e 1 e 2 e 3
and e 4 so I can write over here
er equal to 52.1548
sin omega-t
an angle I am getting over here is
positive so it is a plus 23.57
degree volt
let's represent all the quantities in
phasor diagram so lets represent the
first quantity e 1 is given as 25 at an
angle 0 so the phase angle is 0 and
having the magnitude 25 so it will be
like this it is zero so along positive
x-axis e 2 is 10 at an angle 30 lets
represent e 3 e 3 is 30 at an angle 90
so in anti-clockwise direction it will
make a angle 90 with positive x-axis so
it will be like this this angle is 90
degree if or 20 at an angle minus 45 so
minus means in a clockwise direction
making angle 45 and what resultant we
got 52.1548
at an 23.57
 so it will be like this and the
Angle made by this ER with the positive
x axis is 23.57
so this is how we can represent any
sinusoidal quantity as a phasor and
using a phasor we can get a resultant
phasor out of it thank you
