Hi Welcome to another Fundamentals video. We're going to carry on from our previous series on Dc fundamentals by introducing Dc circuit transients, or more in particular, Lc circuit transients i.e inductors and capacitors, because with our previous videos we've looked at they've just dealt with voltage sources, current sources, and resistors. And when you deal with those sorts of circuits, when you make a change to the voltage of the current, they change instantaneously. And these resistive circuits we've looked at, they're called steady state circuits because well, when you change something, it just instantly changes and then it's steady.

That's not what happens when you introduce capacitors and inductors into your circuit. They actually take time to charge up and discharge and do other stuff. So it's we're not in the realm of steady state anymore. we're in the realm of what's called transient circuits.

So we have to start this off by quickly recapping what is a capacitor, what is an inductor, and then we'll get into series and parallel capacitor. series, Parallel inductors, and then how they charge and discharge and do other stuff. Let's go. Interestingly, it's always referred to as Lc.

It's never Cl. don't know why that is, it's just a thing. Now, the thing with capacitors and inductors is they can actually store energy. Capacitors actually store energy in the form of an electric field across a dielectric material, and inductors store energy in a magnetic field.

And we can actually use these properties uh, to you know, to useful effect as we'll see in future videos. But it's the fact of when you build up the the energy in These devices, then that's why it takes time to build that energy up and then to discharge that energy from them. Whereas something like a resistor, it will be dissipating power when you apply a voltage to it. But it will never store energy as soon.

As I said before, as soon as you remove the voltage. for example, there's no more power in a resistor. It just it just instantly vanishes. Whereas these suckers, they can store things.

And that makes things a bit complicated. Now, a capacitor is just two metal plates separated by a dielectric material, so there's no direct electrical connection. It's essentially an insulator, and that dielectric material can just be air. You can just have two plates or two wires side by side like that.

And that's a capacitor. There's capacitance between me and that camera I'm looking at. Now it's just. you can actually calculate it.

In fact, a common tricky exam question might be, what's the capacitance between the earth and the moon? Figure it out. Anyway, that dielectric material. It can be air. Or it can be any of the Poly.

Put the Kettle On materials for those Poly. Uh, whatever capacitors that you got. It can be one of the various types of ceramic material for your ceramic capacitors or whatever. And then and basically, Aries has a dielectric constant of one.

Most other materials are going to have a dielectric constant greater than that. and that just basically as you increase the dielectric constant, it just increases the amount of capacitance that a capacitor actually has. But anyway, when you've got two plates and you apply a voltage in here, then you'll actually get charge build up, positive and negative charges on both of the plates like that. So capacitor will charge up until uh, the voltage across the capacitor reaches the voltage source and then that becomes a steady state.

But once you you then remove the voltage from the capacitor, that voltage stays on the capacitor, it's stored in there. There's energy or charge stored up in that capacitor, and one of the basic equations that we've actually got is charge is Q equals C times V or the capacitance times the voltage. That's one of the basic electronics formulas you've got to remember. and charge is in coulombs and one coulomb is actually 6.24 times 10 to the 18 electrons.

So it's a buildup of electrons and your capacitance is measured in farads, and a farad is actually a lot of capacitance and V of course, measured in volts, but that's your basic formula for charge. You don't often have to use this, but it's important to know it's one of the fundamental equations. And of course, you can deep dive down into the physics side of all this and things like that, and we won't do that. We're sticking to the practical electronics side of things.

Speaking of practicality, capacitors in series and parallel. I've drawn three here, but you can have as many as you want, or you can have two. And the formula you might actually recognize from our resistor videos: the total capacitance Ct of these three capacitors in series is 1 over all of 1 over C1 plus 1 over C2 plus 1 over C3. And that formula should be familiar to you because it's exactly the same as the parallel resistance formula, except it's kind of flipped now because our capacitors are in series, whereas that exact equation just replace C with R and it's exactly the same for parallel resistors.

And yes, just like parallel resistors, if you've only got two of them, then you can use that uh, alternative formula: C1 times C2 over C1 plus C2 gives you your total capacitance. But if you've got more than two, then that formula applies. And for parallel capacitors here, the total capacitance is just C1 plus C2 plus however many capacitors you got in parallel. And of course, that's the same as your series resistors.

So just think of resistors and capacitors as opposite. The same formula applies just in the opposite case. Easy. Now let's go to back to Capacitors in Series here for a second, because it's important to remember that the total charge uh Q is the same on each capacitor.

It's a bit counter-intuitive. The charge on C1 will be the same as the charge on C2, which will be the same on charge on C3, and that equals the total charge of the circuit. Now with ideal capacitors, when you actually have them in series like this, you will actually get an equal voltage on each capacitor. Like this, V1 will be equal to V2, which will be equal to V3.

Assuming they're ideal capacitors, they're all balanced and everything else. Sometimes you'll actually find what's called balance resistors. Actually, in parallel with series capacitors like this, you'll find these commonly in, uh, like a power supply, voltage, power supplies, and things like that. Just so there's just to help balance out the capacitors due to just you know, practical differences in the capacitors.

So anyway, that's just a useful thing to know and it also helps discharge them as well. Handy! So I'm going to take a little bit of a tangent here. and actually I use the fact that the Ch the total charge is equal also to the same charge on each of these capacitors and that we can actually derive the formula based on this for that using that particular fact. So I've squeezed it all in down here, so please forgive me, I've run out of room.

but uh, charge q equals capacitance times a voltage up there. So as I said, the total circuit charge is equal to the charge on C1, which is equal to the charge on C2, which is equal to charge on C3. You don't add them up. So um, the charge is equal to C1 times V1 is equal to C2 times V2 is equal to C2 C3 times V3.

And if and if we rearrange this formula, voltage equals charge on capacitance. Therefore, voltage 1 here equals the charge Q1 on C1, and voltage 2 equals charge on Q on C and the same for the voltage across 3 as well. Now, if we take this formula, the total voltage equals the voltage across C1 here plus the voltage across C2 plus the voltage across C3. The voltages add up, and if you just substitute that in, I should have an arrow pointing over to that.

Then V is equal to Q on C which is in V1 is equal to Q on C1, Q on C2 Q on C3 Which then translates into our formula. Over here: one on C. Well, that should be Ct. Total one on Ct equals one on C1 plus one on C2 plus one on C3.

So you just move those over and you get that formula: 1 on C1 plus C2 plus C3 And that's how you can actually derive that from that. It's just an interesting little aside, so you can think of the charge as the current in a series circuit. I know this is not a good way, but it's basically the current will be the same for all of them because it's series. Likewise, the charge will be the same for all of them, so we'll work on transients after we've covered inductors.

So let's have a look at an inductor. When you pass a current through any wire whatsoever. any component, any Pcb trace doesn't matter what it is. when you pass current through, there will be a magnetic field.

So that's why I've got a wire here. Just a straight wire like this, you've got current I passing through it. It will generate a magnetic field around it and you might ask which direction is the magnetic field flowing? well. There's a handy little rule which you should remember, which is called the right hand rule and it involves exactly this involves a big a single fonz.

E Thumbs up. It's the right hand rule. Take your right hand like this. point your thumb in the direction of the conventional current flow.

None of that electron current flow rubbish. Conventional currents flow like that. and your fingers like this will point in the direction of the magnetic field. That's called the right hand rule.

So there is a magnetic field around every inductor. That's why you can add like a little ferrite bead. You've probably seen these on circuits. a little wire with a little ferrite bead around it and that is essentially an inductor.

The ferrite B just uh helps sort of contain the magnetic field in there, makes it a bit more uh effective. But anyway, the way you usually make inductors more effective is to have multiple turns. I.e make them into a coil and they can be a physical air coil like that. open any Rf radio tuner, something like that, you know, old school ones and you'll find then they actually have like little just coils of wire like that.

And when you coil them like that, the magnetic fields actually add up and pass through the multiple coils. So that's why you wind inductors into a coil because and and then you can put like ferrite cores through them or you and you can make them into transformers and you can do all sorts of stuff. that's going to have to be the subject of a future video. But yeah, inductors are more efficient when you wrap multiple turns around them.

so the magnetic fields just add up in the coils and it's more better than just a straight wire like that. So just like a capacitor, we can actually store energy inside the magnetic field like this. So when we apply a voltage to it, we'll look at how they charge up and discharge in a minute. But we can actually store energy in a magnetic field so that when you actually release it.

There's a few traps for young players when you release a voltage or the load from the inductor. If voltage can skyrocket, we'll take a look at that in a minute. Anyway, I'm getting ahead of myself. We've got another basic formula.

bread and butter stuff you've got to learn. You won't use it all that often, but You've got to understand. The concept is basically the voltage at any instant in time. That's why it's the instantaneous voltage in volts, of course, is equal to the inductance which is measured in Henry's Once again, a Henry is a very big, just like a Farad is a very, very big value of capacitance.

A Henry Very big value of inductance. and that's multiplied by D I Dt And don't freak out. It's basically that just means the change in the current I over the change in time like that. So some people might write it as you know, Delta I or Delta T or something like that.

But D-i-d-t is just how your mathematicians you know put it, and it's and these are lowercase V I and T to designate that. There's sort of like instantaneous, uh, values. So at any instantaneous point in time on the graph, as you will see shortly, that's what your voltage is going to be equal to. So if you've got a One Henry inductor here and you've got your current change in one amp per second, D I Dt change of current in overtime one amp per second, that'll give you one volt.

Got it? It's a basic formula, and I don't like to do this, but I'll briefly mention it just for a bit of completeness. Then we're talking about Faraday's Law of Electromagnetic Induction, and you can go look at that up. But we get more into the physics side of things. and that is.

E in Volts is equal to minus N, which is the number of turns and D Phi Dt there as it's called. That's the Uh rate of change of magnetic flux in Weber's per second. Now the negative. here.

this is actually lenses law and you can go look up that and that up. But it basically says that uh, the voltage is going to be the opposite of what change actually produced it. So it that's where the negative comes from. Anyway, that'll actually be important in the discharge side of inductors when we look at that next.

So anyway, inductors in series and parallel. It's opposite to capacitors, and it's the same as resistors. When you have inductors in series like this, it's just the total inductance. L is just L1 plus L2 plus L3 in Henrys.

And when you put them in parallel, the total is once again, the same equation. It's exactly the same, except you replace C with L like this in parallel. So if you simply remember your resistance, parallel, and serial series formulas, you'll know that capacitors are opposite Because they're not resistors. They're they're an open circuit.

Whereas inductors are basically the same as resistors. because measure and then go and measure an inductor at Dc and it's practically zero. Ohms because it's just a piece of wire. it's a resistor.

So the formulas actually work out the same. Except your inductors can actually store a magnetic field and you're a pure. resistances can't. Although, in practice, when you're talking about practical electronics, opponent components, every resistance has a little bit of inductance, every capacitor has a little bit of inductance in the leads, and then every inductance has some capacitance across the coils.

And they say, oh, it's just the practicalities of real components is. yeah, they're never ideal, but for most purposes, near enough. And once again, just like we, uh, derive the formula down here, Like this, you can actually do the same thing from your basic art formula to derive this from this. Try that at home.

So now we move on to the transient part of this. We'll first look at Rc transients. and then we'll look at Lc transients ie. resistor capacitor transients.

And as I told you before, there's a charge curve. And there's a discharge curve. Because these aren't resistors. These actually, uh, store energy.

You build up charge or energy into them, and then you can extract energy out of them. So this is our charge curve. This is our discharge curve. We've got a basic Rc circuit.

here. We've got a voltage source V, We've got a switch that we can just, uh, switch to in the up position. Here, it charges up the capacitor through this series resistor r here. So once it's charged up, then we can switch this over to short it out to ground.

and we can discharge the capacitor through that same resistor. So let's take a look at what happens here. So what we've got is capacitance C Resistance r in farads and Ohms, of course. And then we've got a voltage across the capacitor, which is designated uh, V C T That just means that it's uh, changing over time.

Because remember, we're talking about differential calculus here. Basically, Ooh, scary. But we're talking about a change in voltage over time here. Something changing.

That's what differential calculus is. It's just like looking at things changing over time. So in this case, we've got our voltage here versus time and the voltage is going to rise up like this, and you might notice this curve. It's an exponential curve and hence, why? In the formula down here, we've got E, which is an exponential function.

So let's assume that our switch is down here. our capacitor is completely discharged, there's no voltage on it whatsoever, and then we suddenly switch it over up to here, and we've got our voltage of, say, one volt here. Then it's going to charge up until it eventually gets to V here, or one volt. It's going to slowly charge up like this, and that time constant is going to be dependent on the value of the resistor and the capacitor here.

Now, I should have actually wrote this rule on the board, but I kind of ran out of room. So here's the number one rule with capacitors: when they're discharged. When you suddenly apply a voltage to them, they act as a short circuit. Because remember our formula up here: Q equals C times V.

If there's no charge on the plates of those capacitors, it's completely. If it's completely discharged, then the capacitance. It doesn't matter. One microfarad, it can be a farad.

It doesn't. Can be a million farads. Doesn't matter what it is. If you've got no charge, then you're going to have no volts because volts equals Q divided by C.

Zero on C is zero. So that's why as soon as you apply the voltage over here to a discharge capacitor, this capacitor. it's a short circuit. And this is why you can actually get lots of issues with large values of capacitances, particularly in power splice.

Have you ever wondered why When you often plug a mains cable into a big power thump and power supply that has big Dc capacitors there? After the rectifier, you might get a spark or something like that. That's because there's a lot of current flowing because the capacitors are a short circuit. So you're going to get this surge of current flowing. and the current of course, will be because this is a short.

This capacitor is a short circuit will be just V divided by I and that series resistance. in say, a mains 240 volt power supply. There's really not much resistance there. You've got the connectors, the wires, and then you've got the basically the Diode, the equivalent Dc resistance of the Diode bridge rectifier.

And that's pretty much it before it gets to big thumping capacitors. So the in rush current is going to be very large. This is why a lot of power supplies will actually have a slow blow fuse. Because if you put a fast blow fuse in there, the in rush current caused by the capacitors being a short circuit can blow fast blow or quick blow fuses.

So that's why you put a little fuse in there that's got a little inductor which we'll get into. It acts kind of like that, and it's a slow blow fuse that will then prevent that large in-rush current from actually blowing the fuse. Slow blow Fuses Important practical aspect of this, right? So your capacitor is a short circuit that starts out at zero volts here and over time it starts to charge up like this. Now the initial rate of charge will be the quickest and then it will slowly slowly taper off as an exponential function.

And this is our Rise formula. That one of these fundamental formulas you should remember and this formula applies to both capacitors and inductors as we'll see in a minute. But so Vc T, which is what I said is just the change of voltage over time. It's the instantaneous voltage, so the voltage at any instant in time t Here I've written Vc because there's a voltage across the capacitor is equal to the Uh maximum voltage.

So you can think of that as Vmax or your source voltage multiplied by 1 minus E, which is an exponential function. That exponential function is that weird little E to the power of X on your confusor here. Uh, to the power of minus T. So minus whatever the time period is you're talking about divided by capital T.

Not the same thing. Capital T is not the time here. That's little T Like this, Capital T is actually R times C and this is called the Rc Time Constant and you'll see this all the time. And it'll give you like a rough ballpark of how long it takes to charge up a capacity.

And you'll see the Rc time constant in lots of things like Triple Five timer. For example, The formula for a Triple Five timer is 1.1 times Rc the time constant. We might look at why in a minute. So anyway, it rises up fairly quickly and then it follows the exponential curve and eventually eventually after about.

you know, basically after an order of magnitude after about 10 time constants, you can pretty much say it's it's equal to V. In theory, it never gets there, but that's for those math nerds in the real world. it does. And coincidentally, this is the discharge curve that we're going to look at.

the fall curve. But it's also the current because as I said, the current will be a maximum. Just imagine that's not V. Imagine that's I current.

I current will start out as a maximum, which is V on R. You can't get any more than that because of the pesky series resistance. Then it starts out at maximum, and it follows the basically the inverse of this curve like this until we eventually get no current whatsoever and that will be designated I T here. Like that because it's the value of the instantaneous current at any point in time.

Now here's an important thing. uh, to realize this Rc time constant. It's actually an important number. It's actually 63.2 percent of the charge.

Let me show you why. Basically, if you follow the initial charge curve like this up to there. Okay, if if at its initial point, if you went in a linear fashion like that and then you dropped this down here like this, this point here, it'll be equal to 63.2 percent of the maximum charge. And if you take that down there, that is one T and then you'll have two T here and three T and four T and so on.

At that time period, that is called the Rc time constant. But that's how it's actually derived. It's 63.2 percent. It's and like that number means something.

If you ever see 63.2 you know you're talking about Rc or Lc time constants. So assume our capacitor is fully charged up to a hundred percent if we now flip the switch over to here, we start discharging the capacitor like this. So it starts out. this is our discharge curve.

This is our fall curve here. and once again, it's Vct, which is the instantaneous voltage. at any point in time. It starts out at V, which is what we charged it up to starts out at.

You know, if this is one volt starts out at one volt, and then it discharges like this. And once again, a time constant is exactly the same thing. If you follow that curve, it's a bit dodgy, but if you follow that curve, trust me and you'll get to a value of 36.8 Once again, if you see that figure either of those figures there, you know you're talking about Lc or Rc time constants. And there's another formula you have to remember for the exponential decay or exponential 4 in voltage.

Once again, Vc T equals V times exponential to the power of negative T on T. It's exactly the same equation, except there's no one minus and you can see why there's a one minus in there for this. Because V, you've got it. You subtract one whoop.

You start out at 0.. it just means you start out at 0. whereas this one, we don't start out at 0. we start out at V so we don't have the 1 there.

but it's exactly the same equation. Once again, it's negative T, which is the actual time constant in here over Capital T, which is our Rc time constant. Just multiply the resistance in Ohms by the capacitance in farads. Now, we have to get onto inductors.

So I've changed it to Lc transients here, and I've made a couple of changes that looks near identical. Of course, I've changed it to an inductor that's our inductor L there in Henry's and I've got the voltage across of the inductor Vl T and I've got the current through the inductor which is I T here. same resistor, same switch, same voltage source, same everything, and similar as well. Identical curves.

They're exponential Uh curves and once again, the exponential rise here. instead of voltage, we've now got Uh Current equals I I've put I zero. You could say I max I Just the zero means like time zero. So I or I maximum, which will be V on R.

Of course, that'll be the absolute maximum current you can get out of this thing and that's multiplied. It's exactly the same formula minus T over Capital T, which is the time constant. The time constant has now changed. instead of r times C, it's now L on R so you can put substitute L on R in there.

And some people write this equation as uh, minus Rt on L and it's exactly the same thing because if you put that and flip it over anyway, if you rearrange the formula, it's exactly the same thing. and then the exponential decay it's called. i've got a four it should be decay is the better. Uh, the you know, the more traditional, more correct term for it anyway.

I t it's exactly the same. Instead, we've now got instead of voltage, we've got current at time 0 and times the exponential minus t on the time constant and that's it. So we've got to have a look at the graphs now. Now this one is different.

This is now. It's exactly the same graph as before, but it's now the voltage across the inductor here down here. And this is the current through the inductor And as you can see at Time Zero, there is no current through the inductor because that's the rule for inductors. Just like the rule for capacitors was that assume at time zero when you apply a voltage, the capacitor is a short circuit.

Inductors are the complete opposite. Assume that they're an open circuit. this inductant node at time zero. When you flick this switch like this and there's no magnetic field in inductor.

As soon as you flick that switch, no current flows through there at all due to the inductance, the magnetic properties of the inductor, It resists the flow of current until that magnetic field builds up, so it starts out at zero. So the current starts out at zero and it has an exponential rise like that, it's the same 63.2 percent for the one-time constant. Once you get to five time constants air good enough. for Australia, it's you know, within one percent or less.

And because if the inductor is effectively an open circuit, no current flows, then the voltage across the inductor is going to equal V because there's no no current through the resistor. r Ohm's law. there's no voltage drop, so it must start out at oh, I didn't put the maximum in there, but it's V max it should be V and starts out there and it decays like that to zero. Once that inductor is what's called satchel, magnetic field is saturated and it can't uh, you know, hold any more magnetic field in it, then you're going to be at the point over here where it's uh, basically a short circuit because an ideal inductor remember has it's just an inductor.

It has zero resistance in the coil, but of course, all practical inductors have a series Dc resistance, so it's not going to be precisely zero like this. You'll have to use your voltage divider, which we've looked at in previous videos, and then you'll have r with the in series with the Dc uh, resistance of the coil and that's what you're left with If you leave that switch on long enough, it'll eventually decay down to whatever the Dc resistance of that coil is, but in theory, zero. Now, when we discharge the inductor, a really interesting thing happens. Uh, compared to a capacity? remember when we had the capacitor there, it had the charge build up on the capacitor and when we moved the switch over and discharged it and it stayed like the same voltage V maximum and then it, you know it slowly decayed.

The voltage, uh, slowly decayed like this inductors. something weird happens. You remember, Uh, the negative in Faraday's thing over here, which is uh, lenses law and I won't go into details. But basically when that magnetic field starts to collapse because when we switch this, put this switch over to here like this, we've got the energy stored in the magnetic field in the inductor and when you start discharging the inductor, the magnetic field starts to collapse.

and when that happens, this negative sign comes into play. The inductor will do what it has to do to keep maintaining the current flow in this direction. And that means when we were charging up, it was positive and negative like this. But when we start to collapse that magnetic field and discharge this inductor.

ah well. I can't get rid of that. Damn it. This changes voltage like this.

Aha and this is a big trap for young players and but we can actually use this also. uh to our advantage. But if you actually don't discharge it through a resistor like this, if you just like open like, put the switch in the middle, just open it so there's no current flow, the magnetic field still starts to collapse and when it does that in theory, because there's no current flow it generates and in theory generates an infinite negative voltage across that inductor. In practice, it's never infinite, but it's very high.

and this is why you can get large voltage inductive kickbacks and these are very useful in some circuits like your ignition, uh, coil in your car. And that's how you can generate like large spikes and things like that to actually the magnetic fluoro uh ballast. In the old, you know, fluorescent, uh lights. For example, the collapsing magnetic field generates a large voltage which then creates the arc and starts up.

Uh, the lamp. That's how the starters work. Um, in the magnetic fluoride ballast, you can actually generate large voltages by collapsing a magnetic field. And this is why inductors have some uses that capacitors don't But because of that inductors, they're used.

What are they used in relay coils? of course. So if you're dry, if your chip is driving a relay coil like this, and then once the uh, once you actually remove the the current from the relay, then the magnet field of the relay is going to collapse. It'll generate a large negative voltage on the inductor, and well, that could blow your circuit up. So you've got to have reverse diode protection on uh, your coil like this.

So you'll put a reverse bias diode on there so that when this collapses, this is positive. This is negative. Your diode will conduct and it will clamp the voltage across the inductor to negative. Well, 0.6 volts or negative at 0.6 volts.

So that's why you can protect your circuit. And that's pretty darn essential when you're driving relays or any other inductive loads. And you can see how I said before that when the magnetic field collapses, it wants to keep the current going in the same direction. Well, you can see why.

Because if this, let's say we flick this switch to open and there's no load whatsoever. Then the voltage reverses like this. and it wants to flow through the diode like that. because that's your anode, that's your cathode and the current is still going in the same direction.

And to do that, it's got to flip the voltage. That's just what happens. Can I beat the laws of physics? Captain? So what actually happens And go back to our characteristic graphs like this: We have to actually flip these over. Well, this actually becomes V like this.

Okay, but it actually becomes negative V So this will be minus V down here. So it when it flips like this, it'll start out uh with that negative voltage as I said and it'll be the maximum which is equal uh to V what it actually uh was the source actually charged up to and the current will actually start up here. So this will become now I This will become our current and it'll start at a maximum if the current is still positive because as I said, it still flows in the same direction like that, which is different opposite to what the capacitor did when we're discharging the capacitor. Well, sorry, when we're charging the capacitor.

Current flows in this way. but when we're discharging the capacitor, it flows back out this way like this, because the voltage is still like this. Inductors operate opposite. They flip the voltage like this and current still keeps going in the same direction.

Not really intuitive, but that's how the physics of collapsing magnetic fields actually works. So uh yeah, it's it. still starts out. You know if this is like if we charged it up at like an initial hundred uh milliamps? or you know, if it was 100 milliamps up here.

It It started out with 100 if we discharged it through the resistor and it started out with 100 milliamps here. and then it was slowly discharged to zero as the voltage on the coil just dropped away to zero. Ohm's law. But then, like I said, if you leave that switch open, if you've got that magnetic field and all that energy stored in there and you open it up, there's no what does it do it This voltage.

It doesn't go to minus V like this. It goes to as far as it can go and given the physical Uh limits of the actual Uh inductor itself, so you can get like hundreds of volts, thousands of volts when you only charged the thing up. When you, when your source is only like a couple of volts or 10 volts or something like that, you could get hundreds or even thousands of volts. It depends on the magnetic properties of the inductor and the amount of inductance you've got.

So scary stuff. And there's more physics. Uh, two inductors as well, but I won't go into this video has been more than long enough. G's Rc and Lc, uh, time constants.

We covered a lot of stuff. We've been at this for like half an hour or something, so uh, yeah, but it's interesting stuff. Inductors, um, you've got it. Can not only have traps for young players, but it can also be very useful for generating large inductive voltages, which you can actually take advantage of.

It depends what you're trying to do, but yeah, capacitors have energy stored in a in the dielectric in an electric uh field, and inductors have their energy stored in a magnetic field within the coil itself and within the ferrite. Uh, or whatever material is used for the inductors. And maybe we could. uh, go for.

well, probably you have to go further into this if you start going in the transformer theory and stuff like that, which is a video down the track. So the next thing that follows on from this video logically is energy stored in capacitors and inductors. And I've actually done a brief video on this on my second channel. The energy equals half Cv squared like this.

and that half's a little nasty thing when you start talking about charging and discharging capacitors. It's a real sneaky math problem that one. Anyway, I'll link that in down below and probably at the end somewhere. Uh, if you haven't seen that, it was just a test video.

But I decided to talk about this. I'll leave it out of this video. So the rise and decay of voltages and currents in capacitors and inductors. Real interesting stuff.

So you'll be using your confuser a lot for doing these sorts of stuff. And we've only talked about the case where it goes to a hundred percent. If you've got a case where it like only goes up to like here and then starts to discharge again, then well, you've got to substitute, uh, your maximum value for you know, like it's still 63.2 here. So the time constant thing will still happen like that.

It just like starts and ends at a different value. It sort of like, never gets uh to there. and you'll get this in like your Triple Five timers and your other Rc time constant circuits and things like that. and Rc time constants used pretty much everywhere in electronics.

Whether it's in, you know, your micro controller, for example, you might think, where am I going to use an Rc time constant in a microcontroller? Well, for the reset pin, I've drawn it here. If you've got the reset pin of your micro controller, you want your when you power up your circuit, you want your micro controller to have a nice clean reset you don't want to doing. You know, weird stuff while the voltage on your power supply is rising up? No, you want to keep your micro controller in reset and you can do that. Let's say, it's not reset like this.

So if the pin is zero then it's reset. Well, that's what you have a capacitor and a resistor for. Like this, the capacitor will keep your reset pin low for the time constant using the formulas that we've looked at until the voltage on this pin reaches. This will be a Schmidt trigger by the way.

and I've done a video on Schmitt triggers because, well, you don't want to use your regular gate in there anyway. Linkedin trigger video if I remember it and then it'll hold the processor in reset for you know, x milliseconds while the power supply rises up and your process is not going to do funny business. It's going to have a nice clean start. so you know, using Rc time constants for your digital stuff used all the time.

So this basically ends our Dc Fundamentals series that we've been doing. How many five or six videos or something like that pretty much after this, and energy stored in a capacitor and inductor and stuff after that, you pretty much have to move on to Ac Dc Done and Dusted Beauty. So anyway, I hope you liked that video and found it useful. If you did, please give it a big a thumbs up.

As always, discuss down below: catch you next time you.