Tutorial: Electrical impedance made easy - Part 2

hey everyone been here this is part 2 of the video series on impedance but first I wanted to show you what I've been working on this week these work benches even though I've been in this shop for about a year I haven't had a a good selection of workspaces so I spent some time building these benches and I'm actually really excited about this because I've got 20 or 30 feet of linear space now which makes working a whole lot easier okay let's head over to the electronics area and I'll show you what I've got set up today at the end of the last video we had were comparing these two circuits here this one built with a resistor and this one built with a capacitor and I left off by saying well how asking the question how is it possible that the capacitor circuit only draws 0.4 watts using this you know kilowatt power meter and yet the resistor circuit draws 2.2 watts but in both cases the LEDs are about the same brightness so it seems like we're kind of getting something for nothing here and you know the answer is that the capacitor if built perfectly actually is not able to dissipate power so when current flows through a resistor it heats up because the resistor is restricting the current flow through there but that's actually not what's happening with a capacitor in a capacitor you know there's just two plates and once those plates becomes charged up and there's an electric field between them no more currents going to flow so if the capacitor is built with zero resistance parts and the dielectric is perfect there's actually no way that a capacitor can dissipate power so you might be thinking well I said that their impedances for these circuits are about the same I chose the capacitor value and the resistor value such that when we did the math the circuits are almost equivalent well I only gave you half the truth there it's true that the magnitude of the impedances of these circuits is about the same but there's another component to impedance an angle and that indicates whether the circuit is resistive or capacitive and and we're going to get into inductors later but right now let's just concentrate on capacitors so to help you see what's going on in here let's hook this up to an oscilloscope what I've done here is modified our test set up just a little bit this is an isolation transformer so that I can connect our circuit directly to my oscilloscope and I won't fry the scope or myself the trouble with connecting things directly to the wall is that that the voltage that comes out of the wall is referenced to earth ground so if I touched one side of the watt this isn't plugged in right now by the way if I touched one side of the line and that happened to be the hot side of the AC you know current coming out of the wall and I was referenced to earth ground because I'm standing on a concrete floor here I could get a nasty shock and also when measuring stuff with an oscilloscope one side of the measuring system has to be connected to the case of the oscilloscope to the metal box that the you know the scope is built in and if you pick the wrong lead of you can have a you know you can cause a breaker to trip so using an isolation capacity entrace former allows us to connect in one side of the line directly to the oscilloscope ground so let me connect up this circuit here let's look at the resistor first okay so the scope is on and the way it's set up is that channel 1 which is this probe here is connected across the line so basically one side is one side of the transformer and the other side is the other side so it's just going to measure the voltage and this is a 10x scope probe so it's going to divide the voltage here by 10 channel 2 is connected on the other side of this 1k resistor and what this is going to do is allow us to measure the current that's flowing through this circuit here so and I don't have to connect this because I've already got a ground reference right here it would be the same thing as just connecting this here so we're measuring the voltage across this resistor which will tell us the current and we're measuring the voltage across the circuit which tells us the voltage since this is a 1k resistor if we measure a voltage of 1 volt across here that means that 1 milliamp of current is flowing because this is a thousand ohms okay I'm going to plug it in hands out and let's take a look at the scope okay so this is showing us the voltage and current going through the circuit and we're not going to worry too much about units or making a careful measurement here what you should be noticing is that the waveforms are in sync with each other so this upper one here is the voltage and this lower one is the current like I say don't worry about units or something we're not going to make a careful measurement here the thing to notice is just that they're they're absolutely in phase okay now I'm going to connect up the capacitor circuit so I'm gonna unplug it here so now we have something completely different the voltage waveform looks the same addley see that has to be the same because we're just measuring the voltage across the circuit so that's that's basically the same but the current waveform is very different the current waveform is in front of the voltage so this is known as a leading current form or a current waveform so as the voltage is coming up the current is also rising at a faster rate and this makes sense think about what happens when you connect a capacitor to voltage a lot of current flows initially when that capacitor is charging up and so this is known as a leading current waveform so earlier I said that I was only giving you half the story with impedance not only is there a a magnitude associated with impedance but there's also an angle and the angle indicates the offset between the current and voltage waveforms and also tells you whether the current is behind or ahead of the voltage waveform so let's draw this out a little bit it helps to graph it in a purely resistive circuit we can draw this with just an arrow on the x-axis which indicate a purely resistive circuit and the angle here at zero degrees in a circuit that has capacitance we can draw the arrow coming down at an angle here and the more capacitance our circuit has relative to the amount of resistance in our circuit the more that arrow is going to point down into the vertical axis so what these axes actually represent are real numbers and imaginary numbers now I'm definitely not going to get into the heavy-duty math here because I honestly don't think it helps your understanding of how to use this in practical circuits but if you're interested in that you know let me know maybe I'll make a video or you can read about it on your own the reason that you know why not why not just call this X&Y what's the deal with it why choose imaginary numbers the answer is that it just makes the math come out easier so when you get into phaser analysis and all kinds of other things when you multiply an imaginary number by another imaginary number you end up with a negative number and that's important for the math but anyway it's it's you can just think of this as resistance on this axis and reactance on this axis so when you have a capacitor and when you have a lot of capacitance that that arrow is going to be turning down into the into the vertical axis more and if you have more resistance it's going to be closer to the x-axis what happens if you're over in these two quadrants what if you're negative on the real axis that's very unusual that's negative resistance and you know typically it doesn't exist but in certain weird cases it can exist that's if you're interested in that lookup negative resistance that's a whole other topic there for 99 point something nine percent of stuff in the world you'll just be in these two quadrants with real resistance and reactance so let me show you how this this chart relates to our calculation of total impedance for our circuit here so I said if we wanted to calculate the total impedance for this circuit we could use this equation here and we're going to make the nasty assumption that our LEDs behave like a resistor which I know not good but it's a small part of the circuit and it won't make much of a difference and I said that you know you geometry guys would realize that this is how to calculate the hypotenuse of a triangle which is exactly what's going on here so on the real axis we have resistance and in our case it's 1,000 plus 110 110 is what we're going to estimate those LEDs to be and a thousand is the actual resistance from from our little resistor here that's the 1k resistor so on the real axis we can you know say that this length here is represented by a thousand plus 110 and this this part which is the imaginary part is represented by the reactance of our capacitor which we determined to be 5 point 6 K from the from our earlier equation 1 over 2 pi FC but currently here we are the equation for reactance so we can put that one here 5,600 and then you can see that the total you know the sum of these not sorry not the sum the combination of these is the length of the hypotenuse here which gives us the total impedance so let me show you how this impedance chart relates to power factor in volt amps and watts and all that stuff it's actually a very similar looking chart instead of real numbers and imaginary numbers we've got watts which is real power and volt amps which is reactive power on the y-axis here so let's let's look at a couple examples let's say you plugged just a hundred watt light bulb into your outlet at home there the light bulb essentially is purely resistive it has no reactance to it it's just a plain resistor pretty much so we would plot that on this graph by just going straight across on the real power axis watts and we plot out 100 watts no problem just one one line on the graph but if we plugged in our circuit like this which has a reactance to it because of that capacitor we have to plot this angle here just like we did on this graph so we come in like this and our vector here has magnitude in both axes it has watts and volt amps the Watts the real power is a measure of how much power is actually being dissipated in our circuit full tamps just measure how much electrical energy is being pushed back and forth between the power company and your device so if you take your a capacitor and just plug a capacitor straight into the wall every time the 60 Hertz cycle changes the capacitor dumps its energy back into the power lines so what's happening is there's a transfer of power from the power company the generator wherever it is to the power substation into that capacitor the capacitor doesn't lose any energy because there's nothing in there that can dissipate if it's perfect and then the power just goes back to the power company on the next cycle so in theory nothing is lost and you could think of it as you know imaginary power because it's actually not being consumed it's just being pushed back and forth so in a perfect world that would be great no problem just pushing power back and forth is is free it doesn't you know we're not losing anything but in the real world you know wires have resistance to them and so the power company would be very unhappy if all loads were had high imaginary power draw because they would be losing power and all of that pushing back and forth so the power company would prefer power to be delivered in watts only and so this is where power factor comes in so the hypotenuse is known as a parent power and the vertical axis or the vertical component of it is known as reactive power and the power factor is the ratio of real power P divided by the apparent power so having a high power factor just means that this angle is very slight and that most of the load is resistive having a low power factor means that this angle is large and it could be you know in the negative in the lower quadrant here or it could be up here too so all this time I haven't really been talking about inductors I've been concentrating on capacitors but inductors we perform a similar function they limit alternating current flow but sort of in like a the opposite way so capacitors are down here in the lower quadrant and the current as we saw in the oscilloscope leads the voltage inductors are basically exactly the opposite the current lags the voltage but you can treat them in the circuit almost the same way I mean you can use them to limit current we could have built our little circuit here with instead of a capacitor here we could have put an inductor there okay so I've connected up the circuit I've taken that isolation transformer back out so we're powering the circuit directly from the the watt meter here and it's drawing the 0.3 or 0.4 Watts that we saw last time if I switch this into power factor the power factor is only 0.15 about according to this so let's see if that agrees with our calculation okay so here we go so we knew that power factor was the real power divided by the apparent power so what we can say since the voltage is constant in a circuit what we can do is just compare the the real and reactive components of the impedance so what we can say is our estimated power factor should be something like 1110 which is the real component divided by the apparent oh sorry but yeah the apparent the total power here including the reactive parts which we calculated over here to be 5 points m'kay so 5700 so that comes out to be point one nine so you know pretty close we measured 0.15 calculated point one nine we're definitely in the right ballpark here let's take a look at the resistive circuit now so we're measuring power factor again and as you can see the reading is fluctuating a bit in theory this should be one I said with a purely resistive circuit the power factor should be one and the current and the voltage will be in phase together now the reason that this is probably not showing one on the meter is because this resistor that we're using this five point six k resistor is probably a wire wound resistor and that wire winding in there causes it to have inductance and thus reactance and then every time you have reactance of some sort the power factor is not going to be one so unfortunately I don't have a LCR meter where I can actually measure the inductance of that part but that would be interesting to find out it looks like our reading is you know about 0.9 on average another problem that we're having is that this circuit draws so little current that this meter is really straining to to come up with a reading and the way it gets this reading is basically by doing what we did with the scope it measures the voltage and current waveforms and figures out how much of a difference in phase there is and whether the current is leading or lagging so it doesn't it doesn't tell us you know whether it's leading or lagging it just gives us the the angle basically and we have to know from our circuit whether it's capacitive or inductive from a consumer standpoint you actually don't really care about power factor all that much because your your watt meter on the side of your house that measures how much electricity you have to pay for only measures watts so it would be a little bit strange for a power company to charge you for imaginary power right because that power is just going back and forth between the power company and your house you're not actually using that power it's actually the power company themselves that care about getting the power factors high because as I said you you lose power in the power lines so that's actually a loss on the power company's side not on the consumers side it won't show up on your bill so if a residence is you know there's really not much going on I mean basically the power company encourages electronics manufacturers to build things with high power factor but there's not you know they don't come out to your house and measure your power factor however they do do that for large industrial places if you set up a factory I think the power company routinely comes out to measure the factory's overall power factor and if it's too low the power company will insist that you install devices to increase the power factor and in a in a factory setting almost all the loads are like big electric motors which are inductors and the way that you can increase the power factor of a motor is to put a capacitor across it so as I was saying if if a capacitor is below the horizontal axis and an inductor is above what we can do is actually add a capacitor and inductor to make this to bring this arrow back down to level which which would make the power factor high or as close to one as possible so the most common type of thing you'll see for power factor correction is a capacitor strapped on to the side of a motor and that's very often just to counteract the inductance of the motor windings and increase the overall power factor all right well I hope that was helpful I think this pretty much does it on impedance no actually I take that back I think I'll do another one on pins and talk about coaxial cables and impedance matching and that sort of thing let me know if you guys have any specific questions or anything and I'll try to address in there all right see you later bye

Channel: Applied Science

Views: 244,037

Keywords: power, factor, impedance, reactance, correction, capactior, inductor

Id: tZBMfDvWF4U

Length: 19min 46sec (1186 seconds)

Published: Sat Jun 18 2011