Capacitors Are Gaps! How Does That Work?!

thanks to fabulous for helping support this episode hey crazies capacitors make no sense they're tiny physical gaps in a circuit they shouldn't even work but they do work somehow in fact if we analyze capacitors on a deep level we see they're almost breathing energy [Music] before we start discussing abstract things like energy i want to make sure we understand the tangible stuff first capacitors come in a wide variety of shapes and sizes and are made from a wide variety of materials but all of them are designed to make use of a gap in a wire the most basic design for a capacitor is two metal plates separated by an air gap in practice though the gap is usually filled with a solid material called a dielectric wouldn't that close the gap though actually no it's still a gap because dielectrics are insulators then why even include them a few reasons first the metal plates are going to build up opposite electric charges opposite charges tend to attract the dielectric holds the plates apart that means we can put the plates closer together if we want to second anything can become a conductor with enough voltage including air dielectrics tend to be better insulators than air so they help prevent sparks and third the third reason comes down to how capacitors work the simplest circuit looks something like this a battery a light bulb and a couple of wires if they're connected to form a closed loop then charges have a place to go that flow is seen as an electric current through the circuit the charge must flow but if there's a gap charges don't have a place to go which means there isn't a current right well not so fast we might like our physical rules to be simple but as john green would say the truth resists simplicity whether or not a gap stops an electric current depends on the size of the gap we're all pretty sure a big open switch would prevent it but the distance between atoms and a wire is also technically a gap no one ever worries about those tiny gaps preventing a current the gap in a well-designed capacitor is on the order of a micrometer give or take that's a thousand times bigger than atomic spacing but a thousand times smaller than an open switch it's in that vague gray area in between it is a big enough gap to break the circuit but not immediately most of our instincts about electric circuits are based on how they work once they've settled into something we call the steady state in that state the capacitor is definitely a break in the circuit at least when the circuit is dc like all our examples so far in this video but there's a short time at the beginning when you first turn on the circuit when its behavior won't necessarily match our intuitions that's the transient state of the circuit this is the state where the capacitor shines i mean metaphorically not literally if your capacitor is literally shining you're having a bad day anyway the transient state of the circuit doesn't usually last very long if all you've got is a light bulb and a battery it only lasts a tiny fraction of a second fast fast but a capacitor could extend that time dramatically the transient state could easily last a few seconds it's still a gap though isn't it yeah and that's the whole point imagine you've got a battery a capacitor a few wires and a switch to turn things on and off the battery is fully energized so there's a voltage between the two ends voltage is related to energy so we're starting to get a little abstract here just remember that an energy difference or a gradient is what allows stuff to happen all hand ingredients when a battery has a voltage that just means it can do stuff given the opportunity that's all that matters right now with the switch open that voltage doesn't have an opportunity to do anything when we flip it closed everything changes but not right away at first there's no voltage across the capacitor wait that can't be right voltage is what allows circuit stuff to happen if there's no voltage across the capacitor then nothing should happen inside the capacitor hold on [Music] this can't be right what am i doing wrong [Music] [Music] [Music] oh got it okay i am right but there's a subtle nuance i need to explain conservation of energy dictates that whatever the battery puts in the rest of the circuit takes out conservation of energy shall not be violent in a circuit we account for that with voltage but the voltage drop across the capacitor is not necessarily equal to the voltage added by the battery it's very common to assume these wires have exactly zero resistance as electro boom would say they are magic wires in reality though they're not zero resistance no material is exactly zero resistance not even superconductors don't at me we only ignore wire resistance when there are larger sources of resistance when there aren't larger sources we have to include the wire resistance there's no choice which means there are actually two places voltage can drop across the capacitor or across the wires when we first flip the switch closed there's no charge build up on the plates so this is zero there is a voltage applied to the capacitor but all the voltage is dropped across the wires over time though charge builds up and the capacitor takes over once it completely takes over the circuit is broken essentially the capacitor has its own voltage now that perfectly cancels the driving voltage from the battery with no overall energy gradient nothing can happen the electric current stops it behaves exactly how you'd expect a gap to behave it has reached steady state the entire charging process before that was the transient state with these low resistance wires it only lasted a few micro seconds fast fast but if we put a larger resistor in there it could easily last milliseconds or even whole seconds except it wouldn't have charged at all if there wasn't an electric current right correct how is there an electric current across an insulating gap oh it doesn't but we get a current on either side of the gap anyway if it helps you can imagine there's a current in there even though there isn't we've been avoiding talking about fields so far but we can't anymore the behavior of electric charge is inherently linked to the behavior of the electromagnetic field this field usually carries a value of zero but that all changes when electric charges are around you get a non-zero electric field by default but you get a non-zero magnetic field if the charges move around these two fields are often considered one thing the electromagnetic field it surrounds us and penetrates us but it doesn't really bind the galaxy together it is super important for circuits though for example if there's a changing electric field across the gap in a capacitor it'll behave a lot like an electric current the resemblance is so uncanny that we refer to that changing field as a displacement current but to understand how this works the water analogy might be helpful a battery is kind of like a water pump it's not the source of the water it's the reason the water moves a capacitor would be like a chamber with a rubber diaphragm in the middle water can't pass through it but the diaphragm is flexible if the pump is on it's going to push water into the diaphragm as the diaphragm deforms it pushes water on the other side even though the water can't pass through the diaphragm it still moves on both sides at least until the diaphragm is against the wall of the chamber that's when the flow stops a similar thing happens inside a capacitor as electric charge builds up on the positive plate an electric field grows inside the gap that field pushes charge on the other plate causing a current on the other side of the capacitor even though no charge actually jumps the gap it still flows on both sides now this visual may be fairly accurate but it isn't always necessary it's a lot easier to step up a level of abstraction instead of imagining a changing electric field inside the gap why don't we just imagine an electric current in there mathematically that's pretty easy to do this stuff in ampere's law just becomes a secondary current the displacement current we simply swap the field out for an imaginary current and move on if all you care about is the flow of charge that's plenty good enough if you care about where the energy is well that's where the field matters most of the time it doesn't matter how energy moves in a circuit all that matters is that it starts at some source like a battery and gets to where you want it to go that's why what i'm about to tell you doesn't usually get taught in electrical engineering courses but i'm a theoretical physicist physiophysicist physicist i'm a physicist but i'm a theoretical physicist not an engineer so practical spectacle let's go for the deeper understanding we like to think a battery provides some energy to a charged particle then that particle carries the energy around to wherever it's needed energy is provided to charges over and over again until the battery runs out of energy or the bulb is turned off it's a nice simple visual and it might be fine for an electrical engineer but fundamentally it's wrong the energy isn't provided to the particle at all yes there are positive particles flowing around there is an electric current it's just that the energy in this electric current isn't what the circuit uses to do its thing the particles certainly have kinetic energy but that kinetic energy isn't what the circuit uses those charges don't slow down once they settle into a steady flow that's their speed all the way around the current at different spots in a circuit is determined by how many charges are there not their speed the energy the circuit uses to do whatever it does is carried by the fields around the circuit when we're done here you can check out this video from a few years ago if you want a full explanation but here's the quickie version the flow of energy in the electromagnetic field is described by the pointing vector as you can see the electric field and the magnetic field are both involved you need both or there's no energy flow this equation tells us two important bits of information one the energy flowing through a specific point is proportional to the field strengths at that point and two the direction of that flow is perpendicular to both fields in the simple battery light bulb circuit that means the energy flows kind of like this it comes out of the battery into the surrounding field and then flows through the field to its destination what's that look like for a capacitor i'm so glad you asked it looks like this for real for real allow me to explain earlier we saw what the electric field looks like inside a capacitor but here's the magnetic field it wraps around any current in the circuit including the displacement current in the gap remember that displacement current is still a useful abstraction the pointing vector says the flow of energy is always perpendicular to both fields that means it points into the gap from outside as the plates charge up energy flows into the capacitor like this once it's fully charged the current stops which means no more magnetic field which means no more pointing vector which means no more energy flow the capacitor is holding all the energy it can at this moment if the current is alternating the charge discharge cycle will repeat it almost looks like the capacitor is breathing [Music] capacitors are so cool they're a device designed to use a gap in a circuit air gap capacitors do exist but they're usually filled with some kind of solid insulator as the plates charge up an electric field grows inside that behaves a lot like an electric current that current causes a magnetic field to form and ultimately allows energy to flow mind you energy is also kind of an abstraction that means energy flowing inside fields is an abstraction inside of another abstraction but it's really beautiful to look at isn't it so what do you think of capacitors now please share in the comments thanks for liking and sharing this video a special thanks goes out to all my patreon patrons and youtube members for making all this possible don't forget to subscribe if you'd like to keep up with us and until next time remember it's okay to be a little crazy thanks again to fabulous the number one self-care app to help you build better habits and achieve your goals do you have any good habits you want to start or bad habits you want to stop fabulous can help with that self-improvement mental health physical health mindfulness really whatever habit you're looking for it can be 100 personalized for you and your needs maybe you want to drink more water or start doing stretches every morning maybe you just want to set some time aside for reading or meditation my wife has been using it for exercise and food related habits fabulous does track your habits but it's more than just a habit tracker it's actually based on studies done in behavioral science if you 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Channel: The Science Asylum

Views: 309,355

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Id: zYRx6Zub3cA

Length: 14min 51sec (891 seconds)

Published: Wed Dec 29 2021