What is power factor? (Power in AC circuits)

in this video we're going to explore power dissipated in an lcr series circuit and we'll introduce the idea behind power factor but before we look at an lcr circuit let's go back to our familiar pure resistive circuit so let's say we have a resistor of 100 ohms connect across a source an alternating voltage source whose rms voltage is 100 volts immediately the first thing i want to talk about is what is the current in the circuit the rms value of the current is going to be the rms voltage divided by the total opposition that is 100 100 by 100 is 1 ampere now the beauty about rms current is that it can help you calculate the average power very easily and we've seen before the average power consumed by the resistor or you can say it's the power dissipated at the resistor that's going to be just the rms current squared irms squared times r so in our example the average power dissipated would be one square times 100 that's going to be a hundred watt all right now here's my question to you suppose this time i have an lcr circuit whose impedance is also 100 ohms and it is also connected across the same voltage source as before 100 volt rms value rms voltage then the current in this circuit irms the rms value of the current here will also be just like before volt rms voltage divided by total opposition this time we divide by impedance this time it'll be 100 by 100 is going to be 1 ampere so my question to you is what will be the power consumed in this circuit would be the same as before do you think it'll be more than before or do you think it'll be less than before so can you pause and think a little bit about it okay now it might be reasonable to think just like earlier here average power might be i rms squared times total opposition which is z let me use red for that z and we might think okay maybe we end up with the same answer which kind of makes sense right because i have the same voltage same current same opposition as before everything is the same so maybe the power decimation also remains the same but this is not true this is wrong why this is wrong why because the entire opposition does not consume power here's what i mean among lc and r resistor consumes power just like before i square r but what about the inductors and the capacitors they do not consume any power for example if you take a capacitor then what you will find is that when the capacitor is being charged it definitely consumes power it stores energy in its electric field but then when it gets discharged it transfers that power back to the source therefore on an average it does not consume any power and same is the case with an inductor as well on average it consumes zero power which means the entire opposition the entire impedance does not consume power only the resistive part of it consumes power which means even in this circuit even in this circuit the average power consumed would only be the power consumed by the resistor so it will still be i rms squared times r and so would it be the same as before no because before the entire resistance was 100 ohms this time the total impedance is 100 ohms and therefore resistance would definitely be less than that now how much that depends upon the details we don't know but let's say for the sake of for the sake of some example let's say the resistance in this case is just 10 ohms that's totally possible maybe the reactances are very high and as a result i'm getting total impedance to be very high it's totally possible in this circuit that i can have resistance to be only just 10 ohms then in this particular example the average power that gets consumed by this circuit is going to be 1 square times 10 which is going to be just 10 watt at first this did not seem like a big deal to me i mean smaller resistance less power consumed larger resistance more power consumed so what's the big deal this is where the electric company calls me and says you are consuming the same voltage as before same current as before yet you're consuming way less power than before and i say yeah so what's the big deal the big deal is and this is where the electric company is trying to explain to me the problem see when we are delivering electric whenever electric current is passing through a transmission lines it gets heated up so there's some energy loss happening right who's going to pay for those energy losses let's say that energy loss over here was i don't know maybe 20 watt now when i'm consuming 100 watt energy loss of 20 watt the electric company might say fine not a big deal don't worry about the 20 watt energy loss happening you're you're consuming 100 you're paying for that it's compensated i have enough profit margin but over here the energy loss stays the same because the current is the same and the voltage is the same so the energy loss here is 20 what i'm only consuming 10 watt so the electric company says you at this time it's not it's not profitable for me there's so much energy that loss that is happening just for your 2010 watt of consumption and so the person says you have to pay more over here you have to pay for my losses also does that make sense well i'm sitting here i'm thinking that kind of makes sense it's kind of like delivery charges when you're ordering something big and you're paying a lot of lot for it then the petrol charges delivery charges are covered because they're small compared to how much you're paying but if you're ordering say a five rupees pencil i'm just exaggerating then you have to end up paying for the petrol charges and everything right so from a power consumption point of view this circuit has less efficiency compared to this circuit right because for every watt that you're consuming here the energy that is lost that is happening is much higher compared to over here so immediately you might be wondering what do we do about it well the first step is to actually put this in numbers when i say the energy of the the power consumption efficiency is smaller how do i like sort of represent it officially well to represent it what we can do is we can look at this expression for the power consumed and we can try to write this in terms of z okay and i want you to again give a shot to it give it a shot how can you write the power dissipated in this circuit not in terms of r but in terms of z how do you bring z into the picture well i can help you a little bit we can bring back the phasor diagram that we have seen before just to quickly remind you i naught represents the current then the voltage across the resistor which is i naught times r is in phase the voltages across the inductors and capacitors are 90 degrees out of phase and if we are assuming that the capacitor reactance is larger then the voltage becomes 90 degrees behind the inductor and then if we add all the voltages together we get the total voltage and we can now say that total voltage we can represent it to be i naught times z right you can we can represent it this way so what we can do now is we can look at this triangle and try to find the relationship between r z and phi and then substitute over here to get power in terms of z so feel free to pause and try all right so since i want to connect the adjacent side and the hypotenuse i'm going to use cos cos phi is this divided by this i naught cancels out and i end up with r divided by z and since i want to substitute for r i can say r equals z times cos phi and as a result now i can say hey average power therefore equals i rms squared times instead of rl says z impedance times cos phi so this is the same expression as this you'll get 10 watts itself but now we are representing this in terms of the total opposition and this number cos phi tells me how poor or how good my circuit is when it comes to power consumption and so this number is called the power factor okay let's dig a little deeper for a pure resistive circuit can you think about what the power factor would be well here impedance is equal to resistance so z is the same as r r cancels and you get power factor to be one so over here power factor is one another way to think about this is we could say hey current and voltage are in phase with each other so phi value is zero no phase difference so cos zero is one you get the same answer and so this means you get the maximum power consumption your entire impedance is consuming power because your entire impedance is just resistance okay what about circuits that only have inductors or capacitors no resistors at all what with the power factor there well then r is zero power factor becomes zero and that kind of makes sense because we just said that inductors or capacitors on an average do not consume any power so here the entire impedance is not consuming any power and so since there is a current running over here but but there is no power consumption due to that current we call these currents what less current what less current and from an efficiency point of view these are the worst because there will be a heating effect in the transmission lines there will be energy losses but for what you're not consuming any power so this is this is the worst circuit you can think of now of course real circuits will always have all components and so their power factor will always be somewhere between 0 and 1. the closer it is to 1 the better it is better efficient it is when it comes to power consumption and you can now also appreciate why we like resonance here we have seen before that at resonance the impedance is pure resistive and therefore at resonance the power factor is one and so if you're consuming power at resonant frequency then you will be consuming the maximum power okay i want to end this video with a question what if we have an lcr circuit whose lcr and the frequency values are all fixed and it has a very poor power factor what can you do to improve the power factor of that circuit i'll give you a clue if you have poor power factor it means the phi value is very large it means the phase difference between the voltage and the current is very large so the question is how can you reduce the phase difference without changing this but you can always attach something something more to that circuit maybe in series or maybe in parallel okay so that's the clue ponder up on this think about it and maybe discuss with your friends or teachers