Intro to Capacitors | Doc Physics

capacitors are shockingly useful and ubiquitous as a result they they can use it can be used to store energy in fact large amounts of energy even I have some flashlights that operate entirely on capacitors they can store large amounts of energy like this sucker right here this will knock you across the room some of them are used to start motors you'll typically see them in aluminum or some kind of metal sorry some kind of metal can like that a lot of capacitors that you see in circuits are like these these are all electrolytic capacitors right here and these are pretty significant capacitors you also get capacitors made of ceramic and there are super capacitors this sucker is one farad and you'll see that that's an absolutely enormous capacitance but fundamentally a capacitor is really just a piece of metal here and a piece of metal here that's it you don't even need to put any charges on it for it to be a capacitor oftentimes they'll be a wire coming out of that side and a wire coming out of that side in fact that's the circuit diagram for a capacitor yeah looks like a capacitor right so this is another kind of cool capacitor you can see there are lots of plates and they are parallel to each other so if you get more of them depending on how you hook it up you can either increase the capacitance or increase the voltage capacity of the sucker but I want you to notice that there is where the capacitor is really going on look at the spacing between those suckers right there that is a very small spacing so that must be for some reason and we're going to derive the capacitance of a simple parallel plate capacitor there's some reason those plates are so so close together but the cool thing about this capacitor you could see it from right here also the cool thing about this capacitor is that you can vary the capacitance because sometimes these two plates are lined up with each other completely and other times they're completely out of each other so this is only half the plates the other half is over there and this is an extremely low capacitance because there's not much overlapping area and this is a very high capacitance as I bring the plates back next to each other so variable capacitors are also rather important you can use them to tune circuits to do circuit C to get sir to do exactly what you want so if you're designing something particular you want to have a little bit of variation because no capacitor is quite what you want so you put a variable capacitor in there or if you're making a radio or an old-school television you want to be able to get to a certain frequency of resonance in your circuit slosh slosh slosh slosh right like cats walking across a bridge and you would want to do that with a variable capacitor probably as well so let's define capacitance and this is the definition of capacitance capacitance is charged over voltage and that's a super misleading way of writing it absolutely absolutely hate this definition of capacitance it seems to imply that if you put more charge on a capacitor then its capacitance will increase and correspondingly if you decrease the voltage of a capacitor then its capacitance will increase but that's crazy because you know this is the only thing in this equation that is fixed only variable that can't change in fact it would perhaps be much better written like this Q is C times V I prefer to write it like this now this says the charge that's on the positive plate of a capacitor will make this plate positive and what do you say you want to make this other plate negative I'm supposed to use red oh man probably going to have four over there and they'll probably be spread out not in quite the way that I drew them and so the thing is man I don't know how basic to be here no go go look at somebody else for your introduction to capacitors I'm going to get you a little bit into the meaty stuff right here Q is CV says the charge in the positive plate of the capacitor will be the capacitance times the voltage of the capacitor another way of looking at this is saying that the voltage of a capacitor is the charge divided by the capacitance of the capacitor so if I have a large capacitance that means that I have to put a lot of charge on it I have to put a lot of charge on my capacitor in order to get a certain voltage if I have a small capacitance then a small amount of charge will give me a certain voltage so it's really an efficiency of storing charge I'm going to call capacitance efficiency of storing charge without raising voltage much and the beautiful thing about that oh wait without raising voltage much means without raising the energy per charge very much so it's an efficient way to store charge turns out it's also then an efficient way to store energy this reminds me a lot of another efficiency that is represented by the letter C find out what it is put it in the comments let's go on with this definition I'll define a farad next one farad is capacitance and it's the unit over here on this side and then you said Q over V that's the unit of capacitance is a farad so one farad has to be one Coulomb divided by one volt it's a Coulomb per volt okay and remember Gauss's law for a capacitor we actually did Gauss's law for a parallel plate capacitor the cool thing about parallel plate capacitors is if you put a bunch of positive charge on one side and a bunch of negative charge on the other side you get an electric field only where you want it where's our electric field in this case it is only between the two plates and since field is a way to store energy the energy will be stored right inside of our capacitor we're going to be talking about ideal capacitors so we don't have to worry about edge effects and like really there'd be some curving fields over here but whew we do not want to deal with that during our first time through this subject I want to actually investigate how big that electric field is and I want to tell you that the electric field of the capacitor on the inside is simply the charge density on the plates divided by epsilon naught as we found with Gauss's law for a cylindrical Gaussian surface that was right there and well you know what the density on the plates is because Sigma is simply the charge that's on this plate this is going to be plus Q over here and by symmetry I'd like to argue that this will be negative Q they don't always have to be like that but generally under general usage the total charge on a capacitor will be zero it will have some positive over here and some negative over there so this charge density is simply Q divided by the area of the plates get yourselves a little label right here that plate has area a and that plate has area a all right so if we know that this is the capacitance electric field the capacitors electrofield and we know that that's the case then we can just plug this in this is Q divided by epsilon naught times the area of the plates so that's the electric field inside of a capacitor but if the electric field is uniform then we know that oh gosh we know that the absolute I don't want to deal with minus signs right here at all we know that the potential difference between these two plates I could get myself a voltmeter and hook it up right there if I want the potential difference between those two plates it's simply going to be e times D remember it's it's II D right and we can plug in that electric field so we get well Q times epsilon naught area and then multiply the whole thing by D now if we want capacitance we have to go back to our previous equation right here and we can drag it over there and say that the capacitance is the charge divided by the voltage and then we're going to plug in this cool expression for voltage Wow I've got a divided by Q times D and multiplied by epsilon not time's area the queues cancel out and I get epsilon not times the area of the plates divided by the separation between the plates that's our distance D right there as we do this voltage integration right here we're going to be coming to adding more and more electric field and so we're simply going to find the difference the distance between the two plates to be that distance right there and this is the simple expression for the capacitance of a parallel plate capacitor and it's an excellent place to end for the day let me just say a couple things what I want to say I guess I just want to tell you that if the capacitance is larger the capacitor is more efficient at storing charge so the way to do that would be to make large plates okay or to make the plates really close to each other and you can see that these plates right here look right there those plates are very close to each other but they have nothing on these plates right here inside of this sucker these plates are only some handful of atoms away from each other so that has to be done a very careful way and it can easily explode which is called bus and a cap all right

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Length: 10min 10sec (610 seconds)

Published: Thu Jan 10 2013