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