Inductors and Capacitors In-Depth - Exactly The Same Only Completely Different - Simply Put

in my opinion capacitors are fairly easy and intuitive to understand and use but inductors not nearly so much they are a fundamental component and you see them all over the place especially whenever you're dealing with power supplies but they're definitely not as easy and intuitive I consider them a step to learning component rather than step one so I was struggling to learn inductors but as soon as I started taking inductors and comparing and contrasting their similarities to and differences from capacitors all of a sudden it just started to click for me and I realized how incredibly similar these devices really are the unit of capacitance the farad and the unit of inductance the Henry mathematically they are almost the reciprocals of each other and capacitors and inductors are almost the reciprocals of each other as well so this is the way I've chosen to learn and teach inductors and the comparison itself is also instructive so let's get to it both a capacitor and an inductor are short-term energy storage devices where a battery would be a long-term storage device for energy they both will hold little bits of energy in one form or another and then release it they'll hold it quickly and release it quickly and we can use them to implement interesting things like filters and timers but fundamentally they're energy storage devices a capacitor stores energy as charge as in an imbalance of electrons which is what electricity is anyway rather what voltages anyway and the symbol for capacitor basically includes its conceptual construction you can build a capacitor like this and there's also more complex spiral ones with multiple flanges and so forth but basically you have two conductors separated by a gap anywhere you have two conductors and a gap between them that's a capacitor you apply a voltage electrons go in and start stacking up on one side the electrons on the other side gets pulled away as well as shoved away and you get a charge imbalance when the voltage is higher than whatever the capacitor is charged to the capacitor charges more when the voltage is lower it discharges so it wants to always stay the same voltage and this is why capaz are described as devices that resist changes in voltage because anytime there's a change in voltage the capacitor is going to try and take as much power as it possibly can to fix that imbalance so if the voltage goes up higher than the charge it's gonna suck down all the extra power trying to charge up and after the capacitor is only going to see that already amount of voltage it had and the same for discharging when the voltage goes down the capacitor starts dumping it and after the capacitor still sees the higher voltage because the capacitor is providing it capacitance in farad's is basically the capacity of the capacitor as in let's say conceptually one volt is this much of a layer of electrons so you have a layer this thick like icing on a cake of electrons again conceptually this is not a physics channel so this might be one volt and this might be two and this might be three so your capacitance would be how many electrons per volt fundamentally would stay there to make that amount of charge if you increase the capacitance by increasing the surface area then the same thickness layer would have more electrons in it to give the same charge and if you shrink the capacitance by shrinking the surface area then the same thing happens and then you can shrink the dielectric and all this other stuff but basically it's just capacitance is how much charge how much buildup of electrons per unit of potential difference the Volt is in there so more capacitance presumably means more time to charge so let's switch to inductors for a moment an inductor is just a coil of wire we've seen that there's your symbol electromagnet solenoid transformer inductor all these things are basically just coils of wire arranged in different ways and the name is based on the context when we say inductor we mean just a single coil of wire it could be a tiny one inside a little resistor looking thing it could be a big one with this big ol coil it could be half of a transformer it could be all kinds of things but we're talking about just a single coil of wire and you can have them next to each other doing various things but you know that's configuring circuits and stuff when talking about an inductor it's just one coil and we've gone over electromagnets we know that when you put a current through a coil of wire you get a magnetic field an electron has an electric field electricity is electrons moving in aggregate so electricity is an electric field moving in aggregate a moving electric field is a magnetic field so you put current to an inductor you get a magnetic field so instead of storing energy as charge it stores energy as a magnetic field what is the strength of the magnetic field proportional to its proportional to current because the electrons the moving electrons and their electric fields is what's creating the magnetic field if the current is steady then the magnetic field is steady if you increase the current the magnetic field gets stronger if you decrease the current the magnetic field gets weaker so energy is stored in the form of a magnetic field and this is why the inductor is described as a device that resists change in current if you increase the current going through an inductor then it's going to consume the excess energy to increase the strength of the magnetic field and it's actually going to oppose the actual increase of the current it's going to take the excess power trying to push the current but it's not actually going to let the current be pushed until the magnetic field gets stronger and the same thing when the current goes down the magnetic field begins to collapse because the current isn't enough to sustain it anymore and it starts putting out current this is the flyback diode and all that stuff it starts putting out current or forcing more current through to counteract the lower actual current going through it until the magnetic field weakens think of it in terms of inertia if you have a wrecking ball on a chain this big old wrecking ball and you try to push it it's gonna be really difficult to do it's gonna feel like the wrecking ball is pushing back against you but it's actually not there's no Rockets on the other side it's not a living thing acting against you there is technically no force being exerted by the ball on you it's the inertia is called an opposing force but it's not a force the same way like like me lift this pen moving this pin around I'm exerting force on this pen exerting energy to exert this force inertia is not energy being expended there's not energy being drained from the magnetic field to impose this force it's inertia there's not energy being drained from the wrecking ball to actually create an energetic force against you it's just inertia it's just the property of the universe you are expending energy and in doing so you're putting energy into the wrecking ball you're taking energy out of yourself and putting it in the wrecking ball putting it into the system is what it's called and so the wrecking ball begins to move slowly and if you're trying to move the wrecking ball at a certain rate like you have a certain maximum speed in mind you want to push it so fast the closer it gets to that speed the less force you have to exert and once it gets to that speed you're not exerting any force forget gravity for a second just pretend you're pushing it horizontally you're not having to exert any force to push it because inertia is now working with you so that's kind of how an inductor works so you have your wire you have your inductor hooked up to the wire of course that's you know let's do it like this so your voltage is an EMF electro-motive force electro electricity motive motion force the force electro-motive forces the force moving electrons I sounded like a chubby EMU didn't I so voltage is an EMF it causes electrons in aggregate to move in one direction when you have increased the current when the current has gone up are you trying to so you've increased the voltage because that's how you increase the current you increase the voltage so higher voltage is trying to push higher current so each electron is being pushed harder and as a result more of them should go through in a unit time that's increased current but the magnetic field here is based on the current going through so you've increased the current the magnetic field is not strong enough yet and according to lenses law and fancy physics there is what's called a back EMF it opposes the current with an EMF in the other direction there's a voltage you have whatever voltage going across the inductor and then you have the inductor generating a voltage again not by expending energy inertia this voltage is technically not real it is real but conceptually it's not real it's just like the wrecking ball is pushing against you according to Newton's laws but not technically because it's not using energy to do it conceptually it's just inertia it's the same here the magnetic field is not being drained to push against you the magnetic field pushing against you is a consequence of inertia so the current is going to stay the same but the increased voltage the increased force of pushing is going to push against this counter EMF and in doing so it will strengthen the magnetic field that extra is gonna make the magnetic field stronger a stronger magnetic field is proportional to a greater current so now it's going to resist the flow less the back EMF is going to be smaller because the field is stronger so the current will go up but it's still pushing the voltage it wants to make the current higher so it keeps pushing and pushing and pushing just like you pushing the wrecking ball the magnetic field strengthens as the voltage is pushing harder than it needs to for the current current and as the field strengthens this back EMF shrinks and shrinks until the voltage is successfully putting across the current it wants to put across which it matches the strength of the magnetic field and there's no more back EMF and in the same way if you're trying to slow down the wrecking ball the wrecking ball is swinging back at your face and you go stop and the wrecking ball says cool and now you're bleeding but you have successfully removed some energy from the wrecking ball and put it into your face in the same way when you have your voltage trying to put across current and the current is going down the voltage is weaker and the current that voltage would cause is lower than the current proportional to the existing magnetic field strings now you get a forward EMF that's technically helping you assuming you didn't put a backwards voltage but you know basically just the current goes down so now the magnetic field is trying to collapse and get weaker so it's exactly the same thing the current gone down is not providing enough oomph to keep the magnetic field at the strength that was so the magnetic field is going to collapse down to the strength that this voltage will support so in the process of collapsing that energy which had been stored in the Foreman's magnetic field comes back out that way it resists the flow when it's trying to be increased and it aids the flow minutes trying to be decreased the same as the wrecking ball inertia resists you trying to add energy to the system and the process of trying to remove energy from the system is to basically just work against it instead of it working against you now unlike the wrecking ball you don't have to apply a backwards current to stop the inductor it's not physical inertia it's just an analogy basically it'll just charge or discharge strengthen or collapse to whatever the standby current is the stable stationary current is so that's how an inductor works and that's why it's said to oppose a change in current because it literally does with its inertia it provides current when it's discharging and it takes the power away when it's charging so that's the fundamental mechanism and in terms of the unit we usually see L for inductance and the unit is the Henry and you can have a milli Henry or micro Henry or whatever oh I don't know why it's L I haven't thought to look it up but you usually see LRC is inductance resistance capacitance it's just an O so an LR circuit is a simple filter so you have your your coil inductance once again is a measure of the capacity just like a farad is for charge if your inductance is higher than for the same amount of current not voltage but current for the same amount of current the magnetic field is basically going to be stronger for 1 amp 2 amp 3 amp you're gonna have more magnetic strength in there for the same current if you make it longer the inductance goes down if you add coils the inductance goes up and if you make it thicker the inductance goes up for physical reasons let's not get into that but basically both capacitance and inductance farads and Henry's are the capacity of input as in voltage or current to energy stored farads for a capacitor Henry's for an inductor now let's start getting into some of the cool parallels to actually understand the behavior these things and why I think they're really sister devices do you remember this towel that's PI I think I do that every time tau equals R times C resistance times capacitance is called the RC constant this is when you're trying to do timing we say that our time C is approximately 63 percent charge if the capacitor is empty at 63 percent charge up the fall if the capacitors full at 63 percent discharge down to empty 63 percent roughly and that's the time in seconds so tau is in seconds so R times C is the amount of time it takes to roughly get 63 percent charge from empty and we can use that to make filters and such and the charging curve is like that and the discharging curve is like that and there's the shape of it where does this come from when you are charging a capacitor the voltage on the capacitor equals the voltage of the source we'll just say be for battery times 1 minus e to the negative T divided by R times C let's go a piece at a time don't worry I'm not gonna do crazy math let me just explain what this is T is time 0 T equals 0 is you just put the voltage on the capacitor is discharged it's the start of time so time in seconds goes up you're just how much time is elapsed as the capacitor is charging so we have a proportion here this e thing this whole thing goes from 0 to 1 I'm gonna say that now this right here goes from 0 to 1 so at the beginning of time you have VB times zero so the voltage is zero the capacitor is fully discharged at some time you know infinity you have VB times one so the capacitor is fully charged now before I explain why e is in here anything let me just say what if time is RC what if T equals R times C well T equals R times C so R times C over R times C is 1 so this is e to the negative 1 e to the negative 1 e to the negative 1 is approximately equal to 36 some point 3 6 so 36% 1 minus is approximately equal to 0.6 3 or 63% G does that sound familiar that's where that comes from at our time see this whole thing works out to be the voltage being applied times about 63% it's like magic that's why they chose 63% because the math is easy what do you get at five times R times C time equals it's commonly said that five RC time constants means that the capacitor is fully charged it's approximately equal to 99% once you do this it ends up being eat to the minus 5 1 minus that and you get about 99% so we just in the electronics world say oh good enough and in the engineering world they say it's within tolerance so there's complex fundamental electronics physics blood of law that derives this e e is one of those magical constants anytime you see a formula that's got a pie or an e in it you know that you're working with the really cool stuff the really fundamental natural world stuff have you ever wanted to make a mathematician spontaneously orgasm just say 1 plus e to the I pi and then open your umbrella so you see that E and you know good things are happening but basically 1 minus e to this is just something that starts at zero and then eventually goes to one at infinity and that's where our C comes and that's just how the math works they chose RC to be the number that everybody talks about because the math is just so pretty and they said all right it's about 63% that's our C an inductor if I was a Tau as well it's L over R remember that L is the inductance and Henry's so if you multiply farads by ohms you get seconds if you divide Henry's biomes you get seconds do you you get a glimpse now you get a glimpse of hey wait that's pretty cool yeah so what does this mean let's say the voltage of the inductor as in the voltage drop the back EMF the EMF that's fighting because the inductor is fully empty just like the capacitor the inductor is empty so we're gonna apply some voltage to it which means we're gonna apply some current to it magnetic field does not exist currently so the voltage drop the fighting a against the voltage is voltage of the battery times e to the negative T times R over C let me write this like this negative T times R over L I think I've wrote C you get the idea it was supposed to be now so once again e to the negative and so if T is zero at the beginning at time 0 this is 0 so e to the 0 anything to the 0 is 1 so at time 0 the voltage across the inductor equals the full voltage basically when there has been no magnetic field developed at all and you apply a voltage it's going to completely counteract that voltage because the magnetic field corresponds to a current of zero and then at infinity e to the negative infinity ends up being zero so VL equals zero at T goes to infinity VL equals zero so e to the minus whatever is doing the same thing for the capacitor and inductor so what happens at tau equals L over R well L over R and R over L cancels two ones you've got e to the minus 1 again so that equals about 36% so the inductor has charged to about 63% and 36 is about left over from 63 so the back EMF started at 100% and it has gone down by 63% the back EMF has been reduced by 63% that same time constant and so they say once again that five times L over R is about 99% I can write of the way charged and once again you're gonna see this in other forms and usually you won't see if you look this up you won't see this as a voltage you'll see this as a current I just divide it over so its voltage the point is to talk about the back EMF this is the formula for the back EMF so we trust the smart people to have applied Lenz's law and all this other stuff to get this formula correct I'm simply showing you this e to the minus T and whatever which is your tau shows up in both the capacitor and the inductor which is why you have the same kind of time constant the same kind of curve and can use both of them in the same kind of way so what happens if you put capacitors in series if you just have a capacitor and a capacitor and so forth in series let's say series and parallel here that's an R or is trying to be one over the new capacitance or the combined capacitance is the sum let's just do it simpler I won't use the fancy math notation we'll just say 1 over C 1 plus 1 over C 2 and so forth now you may remember this kind of math from the resistors resistors in series is just you add them and then resistors in parallel you reciprocate them all and add them and then reciprocate again same math different thing in parallel when you have a rail and a capacitor across it and then another one like this in parallel the parallel capacitance and I'm not going to derive it this is not a physics course once again we're trusting the smart people you just have the new capacitance is C 1 plus C 2 for an inductor guess what it's the opposite the new inductance for series is L 1 plus L 2 for parallel is 1 over L 1 plus 1 over L 2 inductors in series and capacitors in parallel just add their capacity inductors in parallel and capacitors in series also add but they do it by this fancier formula how do we conceptualize this for a capacitor think about surface area if you have two capacitors in parallel you could kind of think of just sticking their surface areas together and you get double the surface area assuming they're you know don't get into the physics just the analogy I'm just explaining but conceptually you can think in parallel you're just kind of adding their surface areas together so that would just increase the capacity very simply whereas if they're in series you've got you know electrons being pushed let's say your let's say your voltage is like this so negative voltage over here so electrons are being pushed this way and they're being pulled this way but in between them they're being pushed from one to the other and if there's a complex interaction there so it doesn't quite just add up what about an inductor let's say you have an inductor and another inductor so you put a certain voltage across this inductor and you're trying to charge it up and there's going to be an EMF from the battery and a back EMF from the charging process well instead of that let's say you have the voltage across both of them so you've got your EMF where you cross here and they're each going to try and put a back EMF like this so it's kind of like batteries in series this is generating a back EMF which is kind of like having a little battery pointed the other way and so is this so the batteries are kind of in series and so the back EMF back voltages are adding together and in parallel if you have your inductors in parallel the best I can say to you here is just it's complex so you have your your regular EMF here but then you've got your back EMF like this and then it's like having batteries here and do your Kirchhoff's and kick the point is just it's more complicated now I'm sure that was absolutely nothing like the actual physics involved I don't care the point is just to into idiot the point is to be able to understand it without having to fuss about it and then if you want more go take a physics course so what is a capacitor low-pass filter well you have your resistor and then your capacitor and here's your output you measure your voltage drop across the capacitor that's your output voltage and then our time C is your timing that's a low-pass filter what's a low-pass filter with an inductor well you have an inductor and then you have a resistor and here's your output the capacitor is in parallel the inductor is in series and you get the low-pass filter so your square wave becomes a triangle wave and that characteristic shape you may recall like this and then like this and then like this and then like this they both produce it because the charging and discharging curves remember how it was just a voltage multiplied by e to the negative T times whatever times your time they both do the same thing you just hook them up backwards if you have a high-pass filter you have a capacitor in series a resistor in parallel there's your out measured across the resistor if you have an inductor then you have your resistor your inductor there's your out capacitor in series inductor in parallel is a high-pass filter it's just the opposite and that's really cool I cannot stress to you how cool this is to me now you're going to usually find filters made out of capacitors rather than inductors first of all because they're easy to understand second because they're more compact you can get a capacitor a whole lot smaller than you can get an inductor and third they're a little better behaved as evidenced by me hooking up inductors to my oscilloscope capacitors give nice beautiful easy to grasp voltage curves and inductors give the correct curves but the oscilloscope reads them is fairly Wiggly and noisy I'm sure improving the quality of my inductors would help there I've actually ordered a box of really good ones because right now I'm using a homemade inductor and it's not perfect let's just say but the point is they're backwards from each other just like this and there's one more thing you remember reactants when we're talking about a filter with a capacitor a capacitor acts as if it's a variable resistor if you have frequency of a signal and you have reactance now resistance impedance and reactants are all just ohms the name comes from the context resistance means actually a resistor or the resistance in a wire or something like physically resistance impedance is usually talking about inputs and outputs effective resistance there and reactance is usually talking about a passive component acting as a variable resistor in this way but here's the curve a capacitor remember we talked about how it blocks DC and passes AC as the frequency goes down and DC is frequency zero a sine wave is frequency one it's blocks more so your your frequency zero would be infinite impedance not really but you get the point and then your sine would be down here and then as you get more and more of a high frequency noise you have a capacitor that's just letting it through it's acting as less of a resistor for that frequency and then you get your Fourier split and all that stuff so a capacitor has greater reactance which is usually written as XC the reactance because they wanted to write X I don't know reactance of the capacitor equals one over two times pi times frequency times the capacitance as the frequency gets bigger the denominator gets smaller which means the reactance the effective ohms this is ohms get smaller higher frequencies less resistance until you get crazy high frequencies don't just just normal frequency ranges if you get stupidly high frequencies you need special capacitors and whatever because they start to act funky but you know when we're talking about the human range of hearing processing normal signals this is your formula higher frequencies less reactants here's your formula for an inductor the reactance of an inductor is 2 times pi times frequency times your inductance it has the opposite curve an inductor if you have frequency and reactance it actually goes up once again it's the counterpart to a capacitor thus lower the frequency of the original wave of the original waveform coming in signal see the the inductor okay so the the signal is going to change the current back and forth up and down and the inductor is going to resist that as it charges but if you have a slow frequency signal it's always going to have time to charge and discharge before your signal is changing too much so the slower the signal the more the inductor is just going to delay it it's gonna delay the signal it's gonna shift it phase shift but your signal is not really going to change much because it's got plenty of time to resist the flow of current resist the increased flow of current or counteract the decrease flow of current magnetic field strength changes and it stabilizes again the faster the frequency the less time you're giving it so if you have a really high frequency signal then it's going to spend the vast majority of its time giving you strong back EMF s to oppose an increase or putting out strong current when the field is collapsing and it's charging and collapsing really really fast and it never gives it time to really let the signal through so the higher the frequency the more the inductor is going to not let the signal through but if it's real low it'll let it all through a DC signal the current is not changing so for DC if the frequency is zero the reactance is zero whereas here if the frequency is zero take your limit because you can't divide by zero but if you take the limit the reactance is infinite but here frequency zero just means zero reactants in the ideal situation so if you put a DC signal across an inductor it'll just go across an inductor does have a resistance and impedance whatever inside it the usual inductor is gonna have maybe one ohm to 100 ohms ish I'll do a future video on this so there's gonna be a small resistance the small impedance whatever even with a DC signal but small for the most part it's this and look it's just the upside down with the bell instead of the CMS really cool isn't that really freaking cool this is how you understand an inductor and a capacitor or you try to anyway it took me a while and some of it a good bit of it I still kind of say ok the very smart people know what they're talking about but everything about a capacitor and an inductor is just the reverse the inverse the counter of the other they do the same thing in different ways and that's amazing to me because you've got you know electrons being stored across a little gap a dielectric gap versus a magnetic field being charged and discharged by current they're completely different things the only commonalities its electrons in there and yet fundamentally they're so very similar I love it I hope you do too and this is one of those videos where I could definitely have explained this poorly because I've gone for weeks and learned this and try and figure out a way to explain it to everyone else so if I have explained something poorly or not enough or made mistakes let me know in the comments I can always make an additional video I can always fix this video whatever you happen to need so while you digest this information overload I'll be seeing you

Channel: Simply Put

Views: 14,640

Rating: 4.9702601 out of 5

Keywords: simply put, simply, put, inductor, inductors, capacitor, capacitors, in, depth, in-depth, guide, walkthrough, analysis, transformer, transformers, circuit, circuits, electric, electrical, electronic, electricity, electronics, tutorial, what, are

Id: r1t0ZjD9X7A

Length: 30min 22sec (1822 seconds)

Published: Mon Sep 02 2019