okay today's video as you see is entitled AEC capacitive reactance part two and in this video I'm going to go over conceptually voltage and pins and phasor diagrams for our C circuit in the following videos I will go over some work calculation examples but for this video this is the circuit diagram that when you're talking about an our C circuit we're a resistor and a capacitor and AC voltage source this is our our C circuit in this first part of this video I'm going to go over the phasor diagram for voltage so we'll talk about voltage phasor diagram we're going to show you how to determine the voltage of the source and also how to determine the angle the phase angle between the voltage and the current for our C circuits now to review or as an introduction to this video please remember that if you have a purely resistive circuit then the voltage and the current are in phase there is no angle the angle between the voltage current is zero degrees now when we draw the vector representing the current we typically draw that along the positive lakhs so that's the vector that represents the current and it purely resistive circuit because they're in phase the voltage and the current we also draw the vector representing the voltage across the resistor along the positive x-axis because the voltage and the current for resistive circuits the voltage in the current are in phase now that is different of course for a capacitive circuit if you take early capacitive circuit and you should remember that the voltage and the current are out of phase and we have this relatively straightforward device that we can use IC e ice for capacitive circuits that reminds us that for capacitive circuits the current leads the voltage high ECE current leads the voltage for capacitive circuits now we still draw the vector representing the current along the positive x-axis but because they're out of phase and out of phase by 90 degrees and the current leads the voltage by 90 degrees and we draw the vector representing the voltage across the capacitor along the negative I axis like that and this angle is 90 degrees because they're out of phase the current and the voltage the current leads the voltage some kind of people say the voltage lags the current and it's 90 degrees okay now I want to just point out that we can calculate the voltage if we know the current there is using Ohm's law V equals I times R of course and the same thing for our capacitive circuits the voltage across the capacitor is I now we write down X C X being the symbol for reactance and we have a capacitor so this is for our capacitive reactance remember resistors have resistance capacitors have reactants all right now what we're going to do now in the next slide is we're going to draw the voltage diagram the voltage phasor diagram and show you as I said how to calculate the voltage of the source and also the angle between the voltage and the current and since we're going to drawing the voltage phasor diagram on the next slide I'm going to bring my voltage abductors with me okay the current vector would be shown here along the positive x-axis by let that up we're going to be talking about the voltage so this is our voltage phasor diagram we have the voltage across the resistor along the x axis folded across a capacitor because the voltage for the capacitor lags the current then we draw the voltage across the capacitor a lot of the negative y-axis like that now in order to get the Volt is the source and then add these two vectors up okay and because they're vector quantities I can move one of the vectors as long as I'll change this magnitude as direction I can move the vector anywhere I want so I'm going to slide this vector over and see we have a nice right triangle here and the resultant vector the sum of these two vectors which represented by the yellow vector and that yellow vector represents the voltage of the source so this is the phasor diagram for the voltage now we also have this angle right here this angle feed this is called the phase angle this is the angle by which the current leads the voltage only have an RC circuit remember the current in the voltage for resistors are in-phase resistive circuits for capacitive circuits out of phase by 90 degrees the voltage lagging the current therefore when we have an RC circuit the voltage is still going to lag the current but it's not going to be at 0 or 90 to be somewhere between zero and 90 degrees all right now you can see here we have a nice right triangle we in theory with probably node V and our VR and VC R and therefore we can calculate V s using the Pythagorean theorem which tells us that the voltage of the source squared is equal to the voltage across surfaces squared plus the voltage across the capacitor squared and I mean take the square root of both sides you get the voltage of the source is equal to a square root of voltage R squared plus V C squared all right this is the equation that we use to calculate the voltage of the source this is our phasor diagram it's kind of a graphical representation of the relationship between those three voltages all right I want to point out there's one other step we can do to calculate the current if you know the voltages you can use these two equations which we said earlier v equals I times R for resistors D equals I X C for the capacitor I had V R here some of the substitute I are in and the substitute IX in here for the voltage across the capacitor in the square both lined at the voltage of the source is equal to the square root of I squared R squared plus I squared X C squared I'm going to factor out the I solve for I that means the current is equal to the voltage of the source divided by the square root of R squared plus X C squared now we haven't talked about this yet but maybe you know this is that term that is the impedance of this circuit which we haven't talked about a piece we're going to talk about that in just a moment in this video impedance is represented by the symbol Z so I'm just going to simplify the current is equal to the voltage goes for voltage or the source divided by the impedance okay so we'll talk about what impedance is in just a moment I do want to point out here this will start I didn't specify whether this is the RMS voltage or the peak voltage but you should know if you use the RMS voltage here then you get the RMS current use the peak voltage here you get the peak currents please remember to keep those things straight and separate whether you're looking for the rms or the peaks don't mix them up all right now you can see we did the phasor diagram for the voltage we I showed you this equations equation you calculate the voltage of the source we went on the current now we haven't got the phase angle so we're going to do the phase angle right now on the next slide the phase angle the-- this is the angle for an RC circuit somewhere between zero and 90 degrees that the current leads the voltage maybe if you talk about the angle here it's the angle that the voltage lags the current the phase angle fee so that's called and we had two sides of our triangle the opposite side and the adjacent side and that is the tangent so typically this is done with the tangent so the arc tangent of B is equal to the opposite side because tangent is opposite over adjacent using our trig functions if the opposite side is VC in the adjacent side being V R and that's how you can cut like that a angle solving for fee okay all right so that's the mean that's the voltage phasor diagram with the voltage phasor diagram the voltage of the source and the phase angle so now let's go on and talk about the impedance and let's just remind ourselves what the impedance actually is the impedance describes the total opposition to electron flow in an AC circuit so here it says total opposition it doesn't say total resistance or total reactance because as you remember resistors have existence but no reactors capacitors have reactions but no resistance and we have an RC circuits we have to add up in theory all the resistances and all the reactants they only have one of each to get the total opposition which will give us then the impedance which we use a symbol Z to designate the impedance alright once again typically for the resistor because it's in phase with the current we draw the vector representing the resistance on the positive x axis for the capacitor because it lags the current the world lights part then we draw that the vector representing the impedance and takes do not the impedance the reactance of that capacitor along the negative y axis now once again you see you have two vectors we want the total opposition which is the impedance we have to add up these two vectors and once again we use the head to tail method have the two vectors the sum of those two vectors represented by that vector X C and R and then we get the hypotenuse that's Z and that vector represents the impedance of this RC circuit okay and once again we also have the phase angle the phase angle for the impedance triangle and the phase angle for the react for the voltage triangle should be the same angle so you can kind of check your work when you do that you should get the same angle for both of these all right now let's just go through and do that pretty straightforward again it's basically the same process we have the Pythagorean theorem Z squared is equal to R squared plus XC squared square take the square root of both sides Z is equal to the square root of R squared plus XC squared that's the impedance this is how we calculate the impedance once again this is the impedance phasor diagram the phasor diagram for the impedance this we could call that the PR impedance triangle this have a graphical representation this is how we calculate the impedance and then we can get the angle as I said it should be this angle you've got for the velocity triangle arctangent of V is equal to the opposite over the adjacent for that triangle XC divided by art and there you go that's how you calculate the angle fee okay so I think that is everything we wanted to do we talked about the voltage and the phasor diagram we talked about the impedance in the phasor diagram the phase angle and did all that for our ceasers as I mentioned earlier if you want to I can have some links here to some calculations that you can do to see how we do those problems for RC circuits okay so thank you very much for watching I hope you found that helpful if you did please do all the following three things subscribe to my channel give me a thumbs up for this video and leave me a nice positive comment in the comment section below thank you very much for watching see you in the next video you