Capacitors Part 4 - RC Time Constant - RSD Academy

hi welcome to our SD Academy I'm Bob Duhamel today I'm going to talk about capacitor time consonants so naturally I'm going to talk about compressed air so let's look at the way compressed air works let's start out with a air compressor that would be a motorized sort of like a engine running backwards we have a piston and a cylinder that's attached to a crankshaft that's attached to a motor and that makes the piston go up and down in the cylinder and we have some one way check valves to make sure that it sucks air in one side blows it out the other and so we have air going in an arrow coming out and that we're going to send to a compressed air tank let's put a little gauge on top of there that will use a little later to measure the pressure inside the tank so let's say that this pump will produce 100 pounds per square inch now what we're going to do is we're going to put a little air into that tank and what's going to happen you put a little air in you get a little bit of pressure so the pressure gauge goes up just a bit now we put some more air in what happens more air means more pressure so it goes up a bit more we put more air in we get more pressure and we can keep doing that put more air in more pressure more air in and more pressure and we can keep doing that until one of two things happens either we have put so much air in here that the pressure is now 100 pounds per square inch over here so now the pressure in the tank is pushing back at the pump as hard as the pump is pushing at the tank and so it won't fill anymore so the maximum pressure we can get in the tank is the maximum pressure that we get from the pump so we have pumped air into the tank until we just can't pump anymore the other thing that could happen is let's say that this tank was able to handle let's say rated at 100 psi and let's say this can go to 200 psi well if we exceed this by a certain amount and they'll put some safety margin in there but somewhere along the line that tank is going to explode so he can put air into that tank until one of two things happens either we can't push anymore simply because it has the same pressure as our pump or the tank fails and explodes and let's take another look at the way this works let's go back to our 100 psi and go back to zero and just want to make a point here remember that when this is and this is the maximum pressure here I'll just leave that there Oh get that out of the way it might be confusing okay so so there we have the tank and it has zero pounds per square inch what does that mean well remember when you're measuring pressure of any kind you're always comparing one pressure to another so when this has zero psi remember that gauge is measuring the pressure outside the tank and comparing it to the pressure inside the tank and so at sea level the air pressure is approximately 15 pounds per square inch so that's pushing in on the tank and what this is same when it says there's zero psi in the tank it says that inside the tank we also have 15 pounds per square inch pushing out so the gauge says zero when the pressure inside and the pressure outside are equal so remember a pressure gauge measures two pressures and tells you the difference and so once again when it's zero psi simply the inside pressure is the same as the outside pressure which is 15 psi at sea level now let's go ahead and start pumping air in and it's not going to happen instantly we put some air in we're going to get some pressure back so let's say we push in a little bit of air and we get oh let's say 20 psi and we keep pumping now this is pushing back a little bit so it's not going to be able to pump as much air so let's say it took oh let's say one minute to get to 20 psi if we keep pumping how long is it going to take to get to 40 psi it's going to take more than one minute let's just for explanation purposes say it took two minutes to get to 40 psi so now we've gone a total of three minutes how long is it going to take to get to 60 psi well let's assume that now it's going to take three minutes and so every time we go up another 20 psi it takes us another minute so now it's been six minutes so notice that as it fills it gets slower and slower and let's say we put a restriction in the pipe here that's going to slow it down even more so the speed that this tank fills is going to be dependent on how much pressure we can produce and how much of a restriction this hose is to fill it and also it's going to relate to how big the tank is of course have to be double the size of the tank it's going to take twice as long to get to each one of these milestones so the speed of this tank fills depends on how much pressure we can give it how much resistance to the airflow the hose has and how big the tank is so as we fill it up it takes longer and longer because the tank is pushing back more and more and so it takes a certain amount of time let's say we get to get to find me to 100 psi it might take what maybe 20 minutes or so where it took only one minute to get to the first 20 pounds it took another 18 minutes to get to the other 80 psi so it takes longer and longer to fill as it fills up you've probably experienced this when filling tires if they're very low E but they are Chuck on there and it starts to fill up very fast but as it gets close to the pressure you want it slows down a bit especially if the pump is close to the pressure that you want for the tire so if you have a hundred pounds per square inch going into the tire it's going to fill pretty quickly but if you only produce maybe 50 pounds per square inch you'll notice it slows down considerably as you get close to the 30 pounds that is normal for a tire so that's what happens when we fill a compressed air tank now let's look what happens with the electricity and a capacitor so now we're going to start off with a battery and a capacitor and let's put a switch up here just for good measure so I can turn on and turn off the flow and I'm simplifying things a little bit here well complicate them a little more down the road but right now I closed the switch for a certain amount of time and what's going to happen current is going to flow conventional current is going to flow this way and remember from our lesson on capacitors that when we first start to flow current into a capacitor it looks like a short circuit and so what happens is we get positive charges piling up on this plate of the capacitor remember a capacitor is simply two conductors separated by an insulator and the conductors are usually plate shape to give you lots of surface area so these positive charges build up on this side and they drive positive charges off the other side causing the net charge to be higher pressure here lower pressure here so we end up with a charge on there so we get a positive to negative charge on the battery let's see what happens to the voltage as we do that let's say this is a 100 volt battery and we won't worry about resistance right now we'll worry about that later but let's just say things are such that we put a little bit of electricity in and we get maybe Oh 10 volts what's going that way if we put more in we're going to get more voltage let's say but a little more and we get 20 volts this is going to act very similar to the air tank I put a little electricity in I get a little voltage I put more electricity in I get more voltage and I put more electricity and I get more voltage and eventually this is going to get up to our 100 volts so what's happening now this is looking pretty much like a battery remember it doesn't really work like a battery it's just electricity stored under pressure if you will very similar to the air tank where we are storing air under pressure putting electricity into a capacitor is like putting tricity under pressure so as it goes up it gets more and more more and more voltage over here and eventually it gets up to the same voltage so now the battery is pushing this way as hard as the capacitor is pushing that way and we get no more flow so it stops flowing so we can push electricity into the capacitor but a little in we get some voltage a little more in we get more voltage and we can keep doing that until either the voltage of the capacitor now equals our battery voltage and now it's pushing back as hard and so we can't push anymore in or let's say this capacitor is rated at 100 volts and capacitors do have a voltage rating you look at them that will all have a voltage rating on them and that has a hundred volt rating and let's say this is 200 volts now we can get to a higher voltage and some voltage higher than 100 volts the insulation of this capacitor is going to break down and fail and as a matter of fact certain types of capacitors particularly electrolytic capacitors can actually explode when they fail so just like the air take we've put a little air in we get a little pressure a little more and we get more pressure and we can keep doing that until one of two things happens either we just can't push in anymore or the tank explodes with the capacitor we can put a little electricity in we get a little voltage we put more electricity in we get more voltage and we can keep doing that until one of two things happens either we just can't push in anymore or the insulation fails and the capacitor might even explode so there we see in this particular context this capacitor acts almost exactly like an air storage tank to store electricity so like an air storage tank stores air under pressure a capacitor appears to store electricity under electrical pressure or voltage and that's what the capacitor does now also just like I said if are posed in the compressed air system was more restrictive than it would take longer to fill up that tank with air same thing happens with the capacitor if we put some resistance in here it's going to take longer to fill this capacitor with electricity than without the resistance and also just like the air tank if we make that a bigger capacitor it will take longer to fill it up if we double the amount of capacitance we're going to double the time it takes to get to each milestone as we start to charge it up so now let's look at some more practical aspects of how this works let's go ahead and modify this circuit a little but I'm going to draw it just a little bit bigger just to help out here so here's our battery and we're going to put a switch here we're gonna put a couple of switches in here and make a circuit that we can use for a particular thought experiment let's put a resistor here here is our capacitor and back to the battery and I'm going to put another switch here just to help the thought experiment out and let's make this a 1 volt battery and let's make this a 1 farad capacitor and while we're at it what do you think how about a 1 ohm resistor now what I'm going to do is I'm going to close the switch because just like you know that air tank we filled up what if there's already some air in it well then things would have been a little different so to do the experiment correctly we needed to open up the valve and let all the air out of that tank to make sure that the pressure inside was the same as the pressure outside before we started so let's do the same thing here I'm going to close the switch and that's going to make a circuit here so if the battery had any charge on it it will now cause the current to flow in this direction and it will discharge and it will equalize the charge on each plate so that now we put a voltmeter across here and we wait until the voltmeter sees that the voltage is the same on both sides remember a voltmeter is a type of pressure gage and so it is telling us the difference between two voltages so if this voltmeter reads zero volts I'm gonna move this over a little bit so we can see things better so if that reads zero volts that simply means that the voltage on this side of the capacitor is the same as the voltage on that side of the capacitor so flipping the switch causes the capacitor to cause current to flow in this direction until the voltages equalize and now the voltmeter will read zero volts so now we're at a good starting point for this thought experiment let's go ahead and open that switch up so that the capacitor will hold whatever charge we put in now we're going to close the switch and how long are we going to close it we're going to close it for exactly one second and then we're going to open it now what's happened during that one second is we now had a connection through here so we had current flowing this way so electricity is going to go into the capacitor and the voltage is going to increase what's the voltage going to increase to but you're going to think I'll bet one volt not quite in fact those of you who know a little about what I'm talking about probably know exactly where it's going to go so let's look at the numbers I have one farad 1 ohm one volt and one second so I close the switch for one second the voltage increases to what 0.632 volts so one farad one ohm one second one volt that capacitor will charge up to 0.632 volts and let's do that again just to get a number that we can stick in our minds a little bit I'm just going to increase this to a hundred all hundred I'm just going to increase this to a hundred volts and let's do it again because I like the number we come up with let's just charge the capacitor to lure back to zero volts now we're going to close that for one second and now what's the voltage going to be well we increase this by a factor of a hundred so this is going to go up by a factor of hundred so when we had one volt here we got 0.6 two volts here now we're going to get sixty three point two volts so let's look at that for just a second so starting at zero we have 100 volt source here's the key numbers one farad 1 ohm we close this for one second then open it and we end up with 63 point two volts across it I use that because that is sixty three point two percent of the source voltage so if we go back to our 1 volt and we got 0.632 volts once again that is sixty three point two percent of the battery voltage why is that it's just the way it is because of the way we measure resistance and capacitance and time it just turns out that we get this sixty three point two percent of the source voltage once again we close this for one second the voltage increases and when we open it after exactly one second we will have exactly sixty three point two percent of the battery voltage this is called the resistance capacitance time constant so it's a universal constant it's always going to be the same just like we have gravitational constants and other constants in physics this is a constant in electronics it will always be there sixty three point two percent so if we have one ohm and one farad and close the switch for one second we end up with sixty three point two percent of the source voltage that's where that 63.2% comes from now as you've already seen this is going to happen in the first second but what's going to happen when we close this for another second well it's going to not charge this quickly because now this is pushing back a little bit so it's going to hit the next milestone whatever that is it's going to take a little longer or well let's go ahead and take a look at what happens we're going to look at even intervals rather than how long it takes to get to a particular milestone so I'm going to erase this so I can draw a graph so remember what this is we're simply charging the capacitor for a certain amount of time and we have a certain amount of resistance and capacitance we're going to stay at 1 ohm and 1 farad except I'm going to go back to 100 volts so we get these numbers so let's draw a graph here and let's put time marks down here zero 1 2 3 4 5 so that's 1 second 2 seconds 3 seconds 4 seconds and 5 seconds and over here we'll put our voltage so we're going to have a hundred volts in the battery and let's see that's going to be about 50 volts this will be about 75 we're gonna be rather rough here 25 and 0 volts okay so what's going to happen we're going to close that switch for one second the capacitor is going to charge and end up after one second going to end up at 63 point two volts roughly right about looking at this at an angle so I hope I don't get it too crooked right about there so one second we get up to 63 point two volts now what's going to happen in the next second well we have 63 point two and here's 100 volts up here so what's left over we have thirty six point eight volts left to go so what's going to happen when I close that switch for another second so we have to go from 63 point two to a hundred volts that's how far we have to go how long is it going to take to get to the next well what's the soup what's going to happen if we charge for one more second well this is sixty three point two percent of the top voltage so what's going to happen we're going to go sixty three point two percent further so we have a hundred volts sixty three point two volts which is a total of thirty six point eight volts so we're going to go up 63.2% of thirty six point eight volts so we're just going to go sixty three point two percent of the difference left over so let's figure out what that is I should have this memorized but I don't so what do we have we have thirty six point eight times point six three two equals twenty three point two volts so twenty three point two plus sixty three point two gives us eighty six point four volts that's call it eighty six point five so the next milestone let's erase these distractions here the next milestone is going to go up to eighty six point five let's see some definitive to write about what do you think right about there don't need to be perfect here so that's going to be eighty six point five volts or eighty six point five percent so in the first second we go up sixty three point two percent the next second we go up to eighty six point five percent what is that we have gone sixty three point two percent of the remaining difference so we went to sixty three point two percent sixty three point two percent of what's left so what's going to happen after another second all right so we're at eighty six point five what do we have left over so there's our 100 so 100 minus eighty six point five gives us 13 point 5 volts left so we have to go another sixty three point two percent of thirteen point five so what's that times 0.632 equals that's going to be eight point five volts so we take eighty six point five and add eight point five and we get ninety five point zero so our next milestone here let's see right about what do you think right about there 95 volts so we're getting pretty close to the 100 so after 3 seconds once again 100 volts and our resistance is 1 ohm and 1 farad for our capacitor and so after 3 seconds we're up to 95 volts okay so what's the next milestone well we have 95 to 100 this is a 5 volt difference so what 63.2% of 5 5 times point 6 3 2 equals 3 point 1 6 volts more so 95 plus 3 point 1 6 and that's going to be 98 point 1 so we'll just call it 98 now let's call it ninety eight point one just two because we are going to one decimal point there so 98 point one volts so what do you think pretty pretty close to the top there draw this right there 90 98 point one volts let's go one more time we're still about two volts away from 100 volts so let's call that ninety eight point one we have to go well what's the difference between that and 100 so 100 minus 98 point one equals we've got one point nine volts left to go what sixty three point two percent of that times 0.632 equals that's going to be one point two volts so ninety eight point one plus one point two equals ninety nine point three volts so when we get to five seconds we have gotten up to ninety nine point three volts so that is the way the capacitor charges let's just even these out a little bit just because I want them to look even because they really will be that looks kind of even so what happens is when we start charging for the first second it charges pretty quick going up to sixty three point two volts but now it's pushing back so it's not going to charge us fast so the next milestone after another second we're only up to eighty six point five volts which we've gone sixty three point two percent of the remaining voltage now in another second we go another sixty three point two a percent of the remaining voltage ninety five volts the next second we go another sixty three point two percent of the remaining voltage now we're at ninety eight point one and at five seconds we've gone up to I'm gonna try to make that as flat as I can because for all intents and purposes that a little higher there we go just so I can flatten that out a little more there we go we're up at ninety nine point three so for all intents and purposes after five seconds we're pretty close to that hundred volts so what's going to happen after another second it's going to go another sixty three point two percent of what's left over so we're going to get to ninety nine point four ninety nine point four something I need an amplitude so it's going to be pretty flat after this get closer and closer and closer never never actually reaches 100 volts but we get pretty close so we consider that after five seconds that capacitor is going to be completely charged that's if we have one ohm and one farad so I don't want to redraw the circuit I want to keep the graph here so let's see what happens if we change these components let's change the resistance to 2 ohms now what's going to happen well what we're going to find out is that now this takes I want to leave these numbers here somewhere right new numbers in red so now with two ohm's let's put a red two here to remind us that now we've changed to 2 ohms now it's going to take 2 seconds to get to 60 3 point 2 volts it's now going to take 4 seconds to get to eighty six point five six eight and ten so notice that I doubled the resistance I doubled the time it takes to get to each one of these milestones let's see what happens if I put the resistance back at zero excuse me at 1 and but the capacitor at 2 farad's now what's going to happen what we're going to find is that it's going to now take again two seconds to get to our first milestone two sixty three point two four seconds to the next one for to the next our six then eight and then ten so if I double either one of those I double the time it takes to get to each milestone now let's see what happens if I double them both let's put that in blue because we can to ohms and to ferrets now let's see what happens now it takes four seconds to get to the first milestone eight seconds to get to the next one twelve to get to the next one sixteen and it's not 32 I'm going in powers of two there 620 there we go started thinking in powers of two for a second so now it takes four times as long to get to each milestone so if we look at that we can find out that oh there is a formula here that tells us how long it will take to get to each milestone so let's erase that and write that up there turns out that if we take our resistance times our capacitance so resistance times capacitance equals the time it takes our 63.2% of the source so R times C resistance times capacitance tells us the time in seconds that it will take to reach 63.2% of the source voltage so but it's the source voltage well we'll look at some different voltages a little later but let's just look at the official formula here that time which is called the resistance capacitance time constant or an RC time constant is represented by the Greek letter tau and equals resistance times capacitance that is again the time it takes to reach our sixty three point two volts so what if this is a different voltage Oh we'll look at that a little later but we can have a different voltage here and we always reach 63.2% of that so if we now look at our seconds here from our first experiment when this was one ohm and one farad we find that that is now actually our time constants so we'll just put a little Greek letter tau down here that's a rather terrible looking tau isn't it a little till they look there is a Greek letter tau and this is percent voltage so this is no longer 100 volts it is now 100% and these are no longer volts their percentages and no matter what our combination of resistance and capacitance or voltages we can use this formula to predict what percentage of our top voltage we're going to reach after each time constant now remember with the 1 ohm and 1 farad these were seconds but when we had 2 ohms and 1 farad each of these became 2 seconds so one time constant was 2 seconds 2 time constants was four seconds three time constants was six seconds four time constants was eight seconds and five time constants was 10 seconds and if we also doubled the capacitance then each of these became four seconds four eight twelve sixteen and twenty seconds so these are time constants no longer seconds and the time constant will be a certain number of seconds let's see what happens if we change I'm going to leave that up there let's see if we change our values to something more practical let's say we have 100 ohms and 100 microfarads what's this going to do to us I'm going to move this up here just to get it out of the way these are time constants Greek letter tau so now we have remember the circuit we just had a battery a resistor and a capacitor in series so we have now 100 ohms and 100 microfarads so what's that tell us r times C well 100 ohms times 100 microfarads that's going to be 100 times point zero zero zero one so a micro farad is point zero zero zero zero zero one that's 1 micro farad this would be 10 microfarads and there's 100 micro farad so 100 microfarads is point zero zero zero one farad's so that's I do the calculation so here we go 100 times point zero zero zero 1 equals gives us a time constant of point zero one seconds or ten milliseconds forty milliseconds and fifty milliseconds so now we will reach these points at these times so now we have a capacitor discharging pretty fast 10 20 30 40 50 milliseconds we're not even up to a tenth of a second and it's already fully charged just to make sure we understand this let's use something different how about 100 Mike how about 100 ohms and let's say 33 micro farad's another possibly realistic time constant so what do we do is we multiply those together 100 times let's see 33 micro farad's that's going to be point zero zero zero zero three three let's write that up here just make sure you understand so point zero zero zero zero three well that would be three micro farad's and we multiply that by 10 to make it 33 so that's going to be 33 micro farad's it's point zero zero zero zero three three farad's so let's do the math one hundred times point zero zero zero zero three three equals and we have three point three times ten to the minus third or three point three milliseconds so now this is three point three milliseconds this is going to be six point six milliseconds this will be nine point nine milliseconds and nine point nine plus three point three that's going to be nine point nine plus three point three equals thirteen point two milliseconds and thirteen point two plus three point three equals sixteen point five so notice we still have our time constants here one time constant two time constants on to five time constants but now the times are three point three milliseconds six point six nine point nine thirteen point two in sixteen point five so this reaches are essentially full charge after only sixteen point five milliseconds so that's how we can calculate our points of charge using the RC time constant and knowing how that works now let's do a little bit of editing magic I just want to show a different circuit up here before we go back to this graph I don't want to erase it so there's our different circuit so now we have the same circuit but I'm going to do is open the charging switch and I'm going to close the discharging switch we are at the point now where the capacitor is fully charged let's go back to the 1 ohm and the 1 farad and it's fully charged to our 100 volts now I'm going to start discharging let's see what happens to this when we are discharging so there's the circuit let's go back to our board here and what I'm going to do is erase all of these just to reduce the clutter so now we're going to close that switch the discharge switch and that capacitor is going to start discharging so what's going to happen current is going to flow that's going to flow back in this direction away from the capacitor through here and the capacitor is going to start discharging so what's going to happen is this voltage will start going down and after one time constant what do you think it's going to do well 63.2% it's not going up it's going down so we're going to start at 100% in this case 100 volts and we're going to lose 63.2% so it leaves us with 36.8% so we're going to be down here right well what about right about there so now we've discharged down to 36.8 volts or percent in the case of the one in the case of the 100 volts 1 ohm 1 farad will be down to 36.8 volts so this has discharged and I'm going to just avoid writing over my black line so I don't contaminate my pin so now we're down to 36.8 volts so what's going to happen if we discharge it for another second well we're it's 36.8 down to zero we're going to lose another 63.2% of that 36.8 so let's find out what that is 36.8 times 0.632 equals and we have 23.5 so we're going to lose another twenty three point five volts so thirty six point eight minus twenty-three point five thirty six point eight minus twenty-three point five gives us a remaining of thirteen point three volts right about what do you think right about here thirteen point three volts would the circuit we showed or thirteen point three percent of our starting voltage what's going to happen after another time constant okay we're at thirteen point three volts so we're going to lose sixty three point two percent of that so thirteen point three times 0.632 equals we're going to lose another eight point four volts so thirteen point three minus eight point four leaves us with four point nine volts so just about there about five volts that looks about right four point nine now we're going to go another time constant so it's four point nine volts times 0.632 equals that's going to be three point one volts three point zero nine three point zero nam be three point one volts i'm gonna lose another three point one volts so four point nine four point nine minus three point zero nine equals we're going to be to 1.8 volts right about one point eight and then after five seconds we're going to lose sixty three point two percent of 1.8 times 0.632 equals that's going to be one point one four so one point eight minus 1 point 1 4 equals 0.6 six volts or point six six percent and so now it's going to pretty much it'll never completely discharge but it'll get closer and closer and closer so after five time constants in this case of one ohm and one farad it's five seconds we're going to be down to point six six volts and just get lower and lower as we keep discharging so notice that this charge curve looks like the charge curve flipped and if you want to calculate this while we start with our starting voltage and we lose six we lose 63 point two volts down to thirty six point eight volts so there is capacitor time constants which tells us how a capacitor charges and how it discharges and so if we know our resistance and our capacitance we can predict how far the capacitor is going to charge in each time constant so the resistance times the capacitance tells us how long it takes if we're charging our time C tells us how long it will take to reach sixty three point two percent of the source voltage and to calculate the other points we just remember we went sixty three point two percent of our 100 percent sixty three point two percent of what was left over sixty three point two percent of what was left over after that and after that and after that so we just keep going sixty three point two percent sixty three point two percent of what is left sixty three point two percent of what is left so if we ever need to calculate that all out we can do that without any other knowledge and the same thing with discharging when we have a charged capacitor and we start to discharge after one time constant we're down to thirty six point eight percent we lose 63.2% we lose sixty three point two percent of what is left another sixty three point two percent of what is left and on down and that's how a capacitor charges and discharges and that's what we need to know so R times C tells us the time and seconds it takes to move sixty three point two percent closer to where we are going so what uses this information well anytime you need a circuit where you have something happen now and you want something else to happen sometime later especially if that's a fairly short time the quickest easiest way to do that would be with a resistor in the capacitor and time that interval so let's go ahead and draw a hypothetical circuit here let's say we want something to happen after six seconds we flip a switch now something happens six seconds later well let's see let's have our battery there's our switch the resistor and a capacitor and just for practical purposes let's say this is a 100 micro farad capacitor and we want this to get to six point three two volts after let's say ten seconds so there's our switch and let's say this is a 10 volt battery so we can certainly get up to six point three two volts now the circuitry to do this might be a little complicated for this stage of the course using such things as operational amplifiers to make a trigger circuit but we'll just say there's some circuit out here that at six point three two volts it's going to trigger it to go off and we want that to take let's say ten seconds to go so how are we going to figure that out we have 100 microfarads we have 10 volts we need to reach six point three two volts so we need to reach our 63.2% so that's going to be our tau 63.2% and that equals our resistance times our capacitance which we know is 100 microfarads so all we need to do is figure out what resistor we'll put here to give us a time constant of exactly 10 seconds so let's go ahead and do a little bit of algebra magic let's see if we want to put thee we want to find R so we're going to have to put the time up here our resistance equals our time divided by our capacitance so our time is going to be 10 seconds so with a little math imagine I should be able to take our tin and divide it by point zero zero zero one and that gives us a resistance of one hundred thousand ohms let's reverse the math and see if that works out 100 K times 100 microfarads 100 1 2 3 times point zero zero zero one equals that gives us a time cut that gives us 10 seconds so it works out so all we have to do is work the math out to figure out what resistance and capacitance combination it will take to get it to take a certain amount of time for that capacitor to charge and it's just simply T equals RC and this is just like any other of our electronics formulas so just like Ohm's law remember Ohm's law equals IR if we know our voltage we divide into it and so that means that I equals V over R and R equals e over I so if we know your voltage you divide into it if you don't know your voltage you multiply same thing works here we can work that same formula the same way tau where the time constant equals R C so if you if you know your time constant you divide into it so we wanted 10 seconds so we divide it into that so just like that we have if we want our resistance is going to equal our time constant divided by our capacitance and our capacitance is going to equal our time constant divided by our resistance so we can manipulate that formula just the same way we can manipulate Ohm's law that's your simple basic algebraic formula and that's how we've learned how to manipulate that so if you ever need to time something in electronics how do you do it simplest way the resistor and the capacitor use that formula to calculate if you know your capacitor you use that to define the resistance if you know your resistance you use that to find the capacitor and you can find what you need to get the time that you want to take to get to 63.2% of the voltage of course we want to make this last a little longer we would just work the idea appropriately so let's say we want that was we wanted it to take 10 seconds to get here let's say we wanted it to take 20 seconds we would just change tau appropriately let's look at a practical use for how capacitor is charged and discharged that happens every day that you might find interesting in a computer we have a number of chips I'll just show one chip we'll say it's the CPU but this would actually be tied in to all of the digital chips in the circuit to make sure that they all are synchronized each chip is going to have a wire on there labeled as R with a line over it that is the reset line and this would be like a number of chips all of your chips that use the timing of the circuit to operate will have this reset tied together and what we want to do is when we turn on the computer we want the computer to go through a hard reset we don't want things to happen at random you turn on the power it's just going to go to some random state and just not do anything we've got to get the computer to do a hard reset to get it started up you can't just send power to the chip so here's the power line which does go directly to the chip that says plus 5 volts although it'll be probably have lower voltage these days and what we want to do is get a hard reset signal to this when we turn on the power well the line over the R means that the signal that tells it to do a hard reset is zero volts rather than the 5 volts so we want to make sure that when the power comes on and everything stabilizes all the powers of all the capacitors in there have charged up remember it's gonna take a little while for everything to happen because we have the capacitors in there they're gonna take a short time to charge up and for everything to stabilize so we want that chip to do a hard reset after everything is stabilized so what we're going to do is put a capacitor across that line going to ground and we're going to run the power to that except we're going to do that through a resistor so now what's going to happen is when we turn on the power this goes to our power supply I'll show as a battery when we flip that power switch the power is going to go to all the circuits all the capacitors are going to charge up and stabilize but this is going to be what remember when you first start to charge a capacitor the capacitor is zero volts so I turned it on that capacitors at zero volts and as long as it stays below a certain threshold let's say in this case it's one volt so this chip recognizes anything less than one volt as zero as a logical zero so that's the threshold of one volt so we want this to remain a logical zero or something less than 1 volt long enough for everything to stabilize before it comes out of that and allows the chip to start it's hard reset cycle because as soon as this reaches a logical one it will do the reset cycle so it's start has to go to zero but then when it comes out of zero it does the reset so we turn on the power everything stabilizes this is still held at zero volts or a logical zero it starts to climb up and we've already said that when it reaches one volt that's going to be recognized as a logical one and it will start the reset process all we have to do is make sure that our resistance and our capacitance is such a combination that it takes maybe a second long enough for everything to stabilize before this voltage climbs up above 1 volt so there's a practical use for RC time constant that I know is used every day to restart a computer so there's a practical use for RC time constant that's used in a circuit we use every day every time you turn on the power to your computer that capacitor holds this reset line at a logical zero until everything stabilizes that allows us to climb up and once it comes out of zero it does the reset cycle so a quick recap of what we've learned here get some of the clutter out of the way leave those up there and I'm just going to put a some basic symbols here our voltage our resistance and our capacitance so if we put a little bit of electricity into capacitor we get a little voltage we put more in we get more voltage we put more in we get more voltage and we can continue doing this until one of two things happens either the voltage in the capacitor has reached the voltage of our source and we can no longer charge it or it exceeds the capacity of the insulation and the installation breaks down and the capacitor might explode and that's how a capacitor charges and to predict what voltage it will be at a particular time if you take your resistance times your capacitance it tells you the time in seconds it will take to reach the magic number of 63.2% of the source voltage and to find out how much it does after that after each time constant we go another 63.2% of the remaining voltage whether we're charging or discharging charge we go up 63.2% each time discharging we go down at 63.2% every time so if you found this video useful and informative please give me a thumbs up down below that's very helpful to the channel and it helps other people trying to find these kinds of videos find them and I want to give a big thank you to everybody who's commenting on my channel I am receiving lots of great comments I wish I could respond to all of them but I only have time to respond to a tiny fraction of them so big thank you I really appreciate these comments and if you'd like to help put these videos online and help keep our ski Academy available you can comment on these videos put a link on your blog or website or if you can go to patreon.com/scishow rst Academy and pledge a donation and a big thank you to my patrons at patreon and a big thank you to everyone for watching

Channel: RSD Academy

Views: 7,710

Rating: 4.9915433 out of 5

Keywords: Basic electronics, electronics school, free online classes, electronics classes, learn electronics, learn electronics technology

Id: 3iZwfYAeqQI

Length: 51min 41sec (3101 seconds)

Published: Tue Jan 21 2020

Reddit Comments

[u/danlbob]

This guy is great. And it's like my dad explaining electronics.

[u/timejoannah]

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[u/Foodei]

Two thumbs up.

[u/Drum_computer]

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