 This video is going to be a complete walkthrough of a DC Circuit that has a capacitor, which is this little filler right here and a resistor in it right now Nothing's happening. We've got the switch open, but when we close that switch some stuff's going to start to happen Now we've closed the switch now if you remember from the inductor video when the inductor switch is closed Current starts to race through the circuit and it gets up to a steady state That is not the case in this case. We have a capacitor here. So what's happening is we are building charge I'm going to assume again, you know, but this is just a quick little mini lesson. We're going to take the electrons here We're going to dump them on those plates. We've got the holes here. We're going to take them over to that side We're going to get current flowing for a brief amount of time and then once this guy charges up the Capacitor charges up to be the same voltage that the battery is then current stops flowing So what we're doing here is we are setting up voltage on the plates as opposed to the inductor So if I did that same little chart that I did in the inductor video I've got this guy going across like that and that I Start out at zero volts and I'll work my way up and then I'll reach a steady state voltage We're not even gonna call it steady state voltage. It's just going to be the voltage at the capacitor Now that's the thing with this one. We have to remember that when we're doing our calculations We're calculating the voltage at this capacitor capacitor So let's throw some values at this I've given the capacitor a value of a hundred microfarads I've given this resistor twenty five ohms and I've given us 120 volts source voltage and what we're going to do is we're going to work out tau So it's the same thing as an inductor. It takes five tau to get up to a full charge capacitor So we're going to work out what the tau is the time to the full charge of the capacitor then we're going to walk through some voltages we're going to use a Very familiar formula for this voltage at the third tau. We're going to talk about this voltage at the third tau We're going to talk about what happens to the current at the third tau And then we're going to talk about the w with the energy stored in the electrostatic field in between the plates So let's take a quick look at the formulas that we're dealing with with this walk through So here we go our tau with our tau with the inductor It was L over R with the capacitor. It is R times C. We have no L. Obviously, so we're taking the resistance We're multiplying it by the capacitance to get the tau or the time constant Then we have to remember we take five of those five times tau equals the time it takes to fully charge that capacitor Then we get this guy here this one minus e to the negative X times V source And this is important equals your capacitor voltage not your resistor voltage You're going to want to use that as your resistor voltage. Don't do it. It's your capacitor voltage So one minus e to the X that minus X sign that is your time constant So if you're trying to figure it out at the first time constant, it is one minus e to the negative one Second would be one minus e to the negative two Third is one minus e to the negative three and so on and so on that one just stays there as one You don't change that at all Then our voltage at the resistor we have to obey Kirchhoff's law So our voltage at the resistor is going to be once we figure out our voltage at the capacitor You're going to take that and subtract it from the source and that gives you your resistor voltage and then to determine the current Well, it becomes quite easy once we have the voltage of the resistor We're going to divide up by the resistance because e over i Sorry e over r equals i. It's just ohm's law and Then the energy stored is just w is equal to point five c v squared Much like it was for the inductor, which was w w equals point five li squared So these are the formulas we'll be dealing with with our walkthrough. Let's take a crack at it So here we go our first item on the list here tau So to get the tau all we have to do is go 100 micro farads So you're going to put that as 100 to the negative 10 times 10 to the negative 6 And you multiply that by 25 and then you're going to get 2.5 milliseconds, which is perfect now time to full charge all we have to do is take this number here and Multiply that by five because it takes five time constants to reach full charge. So five times 2.5 gets us 12.5 milliseconds So we got those two down now all we have to do for the voltage at the capacitor if you want to go back Like a minute and look at that formula part of this video as we go 1 Minus e to the negative 3. Let me write that out just so we get that wrapped in our head here Let me just make my pen a little bit bigger 1 minus e to the negative 3 And we're going to multiply that by the source, which is 120 volts We do that and we get our voltage at the capacitor at the third tau that works out to be 114 volts So we're almost done guys. This is getting easier and easier as we go now. We know that we have 114 volts here We want to figure what the voltage is here Well, we know if our source is 120 volts there and that is 114 volts that leaves us with six volts That it has to be across that guy there Now let's talk about the current We can't work out the current when it's across a capacitor that won't work out for us But we can work out the current across the resistor because we have a voltage on the resistor Which is six volts and we have a resistance at the resistor, which is 25 volts Using ohms law we would take 6 divided by 25 to get what our current is which is 240 milliamps so at the third tau our current is 240 milliamps so it's dropping and then by the time we get to the fifth tau Remember, we will have no current in a capacitor circuit The only time current flows in this circuit is when the plates are charging once the plates are fully charged current stops flowing Only thing left now is this energy stored in the electrostatic field between the plates We're just going to go point five times C times V squared and we get 720 millijoules and that's it We've worked out a volt drop across the resistance We've worked out the volt drop across the capacitor and we've worked out the current flowing in the circuit And we've worked out the energy stored in between the plates. There's nothing else to it Now the only thing to mention now is when we open this switch when we saw an inductor when we open the switch The current would drop like it was hot, but in this capacitor. We're not dealing with the current We're dealing with the voltage specifically. We're dealing with the Electrons on the plates there when we open that there's no place for those electrons to go So a capacitor could actually Theoretically hold its charge until somebody came up and licked that or touched it or some sort of discharge resistor was put across that To get rid of those electrons. We will talk about that in another video. We will be putting in a discharge resistor See you on the next one