in the last video we figured out the currents resistive current inductive current combine them together pythagoras lee and got the total current figured out the impedance now we're gonna deal with power apparent power measured in voltage that's what the circuit needs to provide true power across the resistive component that's the working power the real power doing the real work the heat the light the motion and then we have the reactive power voltage reactant in this case from an inductor a reactive component and that power is stored in the inductor and then released and stored and released it's not doing any actual work okay but the circuit still needs to provide it and what did i draw it down here last time we had the resistive current in phase with the voltage and the inductive current ninety degrees out of phase what I took was the sum of the two and it is neither in phase with the voltage nor out of phase 90 degrees it's somewhere in the middle the resistive current tried to pull it back in phase the inductive current trying to pull it out to 90 and because there's a little bit more inductive current than there is resistive current it's pulled a little more out of phase probably closer to 90 than it is to zero but we're gonna figure that out right here we'll figure that out from the triangle and see how that relates because it power wise what we have is when both voltage and current are positive II times I I've got positive power when they're both negative e times I both negatives result in positive power but when one is positive and one is negative I have this negative power a positive times a negative number is negative that's negative power so that's the area of wasted power that the positive power minus the negative power and what do we end up with and in this case it's it's net positive so no problem that's due to the resistor if it were purely an inductor it would be half positive half negative no real work would be done okay let's figure the numbers how do we figure them out Ohm's law power it's a function of bolt and amps or B squared divided by ohms or N squared times own throat we can use any Ohm's law so let's punch them in a times I is probably the simplest for power let's punch them in for all three of these and figure out what our power numbers are when we get these numbers or seventy seven point six volt temps true power measured in watts 288 and voltage reactive I've put the little L because they're provided by an inductor not overly important in this class but as we start to combine the components we'll want to know what power comes from what component and that's 380 1.6 VARs draw the triangle for those what will that triangle look like so we haven't drawn this way we know that the true power because it's from the resistive component will be on the horizontal line resistive components always on the horizontal line because they're in phase voltage and current the reactive component ninety degrees out so we put the VARs vertical and the VA is the vector sum of both so if you look at your formula sheet let's take a look it would be Pythagoras your apparent power is the watt squared times your bar squared similarly we come up with a hypotenuse hypotenuse always represents the total circuit values so we have our power remember power factor that efficiency of how much of the power that I'm putting into the circuit is actually doing real work it's a ratio of watts divided by Bolton's and if we take 288 divided by four seventy seven point six what do we end up with little over sixty percent so of the power we're putting into this circuit a little over 60 percent of it is doing real work and there's now this relationship between my power factor and angle theta it brings in your sines and cosines and all those things because what did we essentially do if I want to find this angle for power factor we took this side over this side that's my adjacent side over my hypotenuse adjacent over hypotenuse that's cosine but if I know the angle I can get cosine of that angle will give me the ratio of this side to this side but right now I know that ratio sixty percent or point six zero three is the ratio so how do we work that backwards here's how we do it regular if I knew the angle I would just do cosine and the angle and get adjacent over hypotenuse I would get that ratio on both sides we talked about proportional triangles I could have done this with the current however I know the ratio that ratio adjacent divided by hypotenuse is sixty point three percent or written decimally that would be point six zero three and if I were to do cosine negative one which is basically inverse cosine or arc cosine you would hit second function and then the cosine button and you would see this second function cosine button that's what you see you put in the ratio or you can do a divider you can do 288 divided by four seventy seven point six we know what that is already close the parenthesis if you want hit equals and what do you get 52 point nine degrees that's that angle we can tell that it's going to be more than 45 because this side is longer than this if they were both equal it would be 45 so we can kind of guess is it going to be less than 45 or more than 45 and sure enough it's a little bit more and what does that mean back here the total current is shifted 52 degrees 52 point nine degrees the current is lagging the voltage and there we have it power numbers and how they relate to power factor the efficiency how much of the power I'm putting in is doing real work and my angle-theta could do this for any of the triangles and that relates to my sine waves and then the current that the total circuit value is going to be shifted 52.9 degrees we've stressed that point here they're in phase here they're out of phase by 90 degrees but the combination is somewhere between zero and 90 degrees somewhere in the middle one last point is trying to light through up but I had the current triangle facing down okay it just has to do it as we add in capacitors down the road we've got to figure out which power triangle goes up in which power triangle goes down so generally speaking and you may see it different in some texts but generally speaking we're drawing the inductive triangles inductive power triangles pointing up and we'll find out that capacitive once an X AC will point down but remember the triangle appoints down in this class with RL circuits is your current triangle in parallel had to do with voltage being the reference and across an inductor the current hanging behind 90 degrees but when we get to power inductive ones we point up