If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:11:28

i have a battery connected to a bulb via a switch i close the switch the bulb glows open bulb doesn't glow close bulb glows no surprise over there but now let's attach a coil wrapped around some metal in series with the bulb and see what happens ready three two one close whoo now we see the bulb takes some time to glow why is that well let's find out wait did you see that seriously what is happening so with the coil in series we saw that when we close the switch the bulb takes some time to glow to its full brightness from this we can infer that the current takes some time to grow to its max value the value given by ohm's law maybe one ampere let's say that's the maximum value which means the coil is for some reason dealing it's slowing the rise of the current but why is it doing that well let's investigate if you pause the animation over here we know that there is some current running in the circuit it's not maximum value yet but there is some current and that current is of course going through the coil and we've seen when we have current circulating through some coil it generates a magnetic field we've seen this enough number of times now now what's interesting over here is that this current is increasing remember we are not at the max value we have paused the animation the current is going to increase which means the magnetic field that is produced over here also tends to increase this means the flux is increasing and we know from faraday's law that whenever there is a change in the flux the coil will induce an emf trying to oppose that change so over here in this coil there will be an emf induced opposing that change in flux okay that's a lot to take in so let's let's slowly write this down so what we're seeing at this moment is that there is a changing current let's call it di or delta i because of that changing current because current is producing magnetic field and there is a magnetic flux there is a changing flux over here the flux is changing and we know from faraday's law that that changing flux causes the coil to produce and or induce an emf and that emf always tends to oppose the change okay so what does this all mean well if you get rid of this middle man then this basically means that whenever the current changes through a coil the coil will produce an emf trying to oppose the change which means if you try to increase the current through the coil it will produce an induce an emf 2 and tries to decrease it if you try to decrease the current you will use an emf and will try to increase it remember the coil has no problems with the current itself once the current reaches the maximum value the coil does not induce any emf the coil is happy it's the change in the current that's where the problem lies so whenever you try to change the current through any coil you induce an emf and tries to oppose that change and this ability to resist changing currents by inducing an emf is often what we call inductance and that's why coils are often called inductors to be more precise we should call it self inductance because the changing current and the opposition they're both happening in the same coil so the coil is sort of kind of like opposing itself and that's why it's called self-inductance so more inductance means more ability to resist the changes in the current so it's kind of like an inertia in fact that's why inductance is often called electrical inertia resistance to change but change of what change of current now before we get back to our story let's think about how much emf or how much voltage is this coil inducing due to the changes in the current we can figure that out using faraday's law faraday's law says that the induced emf in any coil equals negative n d phi over dt where phi represents the magnetic flux you can call it d phi b or dt this basically says that the induced emf depends upon how quickly the flux changes if the flux changes very quickly a very high emf is induced and it opposes the change in the flux now in our case the flux is generated by the current more current more magnetic field more flux so we can say that in in an inductor or in a coil flux magnetic flux is proportional to current so you know what we could do we can write this to be equal to negative d i over dt we're basically saying the flux is changing because the current is changing right and it's proportional so there should be some proportionality constant and that constant we often like to call l and that l represents the self inductance so this means if the current changes very quickly the emf induced is very high if the current changes very slowly emf induce is very low the current doesn't change at all no mf is induced and for a given change in current a given rate of change of current notice the emf would be high if the inductance is very high so if the l value is huge it means very very high resistance to changes in the current very high emf in induced if the if the inductance value is low or zero notice it doesn't matter whether the current changes or not there will be no induced emf so this thing represents the inductance and very quickly we can work out the units of the inductance feel free to pause and try figuring out yourself so the unit of inductance becomes emf which is volt divided by amperes per second divided by amperes per second and the second will come on the top but we often like to write this henry named after joseph henry who was another person who independently discovered electro magnetic induction and just like capacitances or resistances which only depend on their geometry and the material used and it does not depend upon the current and the voltage similarly inductance also only depends on the geometry depends upon the number of turns you know what is it turned around the material used over here but it does not depend upon voltages or currents and in future videos we'll we'll calculate we'll see how to calculate the inductance of a coil or a solenoid but it does not depend upon voltages or the amperes with that now we can get back to our original experiment so what happens the moment i close the switch well the battery says hey i want to increase that current from 0 to 1 ampere as quickly as possible so there is a di or dt coming and the inductor says ah i hate changes in current and so it opposes that change and the the way it does that is it induces an emf or it produces a voltage and since it's opposing the battery because it doesn't want the current to increase the voltage comes this way with the plus on this side and the negative on this side which opposes the current but then the battery says all right okay i will i will grow the current a little slowly so di by dt reduces and as a result the induced emf the voltage induced starts reducing now not very carefully i did not say the current reduces the current is zero to begin with how can it reduce but di or dt the rate at which the current is growing that slows down the battery basically says okay inductor i will increase the current a little slower so the inductor gets a little less mad and as a result of that now the current starts growing and as the current keeps growing the dio dt starts reducing more and more i mean becomes smaller and smaller and as a result this induced emf starts becoming smaller and smaller the opposition starts becoming smaller and smaller and that's why the current can start becoming larger and larger and that's why slowly and steadily the bulb starts glowing and eventually eventually once it reaches that max value of one ampere the current no longer changes di over dt becomes zero and once that happens there is no longer an induced emf the inductor is happy because the current is not changing anymore remember inductor has no problems with the current it's the change in the current that the inductor has a problem with yes i'll keep saying it until you get it because this can be confusing okay and i hope you agree that if the inductance value was very high if this was a large larger inductor then it would take longer time for the current to rise to its maximum value because the opposition would be so much stronger okay so now the current is running at its max value no longer changing the inductor has no longer any effect on the circuit and now i try to open the switch what do you think is going to happen based on what we learned can you pause and ponder upon this and think about what's going to happen if i open the switch now all right let's do it together let's open that switch so so far the inductor was calm the moment we open the switch the battery just gets disconnected from the bulb and the battery says let's let's get let's get the current back to zero and the inductor goes wild the inductor says are you kidding me i hate changes in current now the d i by dt is negative the current is trying to reduce and that too it's an incredibly high value the current is trying to go to zero almost instantly the inductor gets mad the inductor induces a much higher emf but this time in the forward direction can you see that negative times negative becomes positive so this time the inductor is trying to support the current remember inductor never had a problem with current it always has a problem with changes in the current so the inductor tries to maintain the current but wait the circuit is broken there is air in between there's so much resistance how can it do that well it generates a huge emf a huge huge emf is now coming and as a result of that it's trying to maintain that current but wait where would the charges go the charges don't have anywhere to go the circuit is broken because the inductor is pushing pushing pushing the charges get accumulated over here a lot of positive charge gets accumulated a lot of negative charges will get accumulated over there and eventually there will be a spark but the inductor can't maintain that eventually di by dt goes to zero this goes to zero and the current dies off that's the story and during that last second when the inductor got really really mad the voltage that it generated was incredibly high it can be hundreds or even thousands of volts and therefore it's incredibly dangerous to try and switch off a circuit where there are huge inductors involved it can cause nasty sparks and so that's the story of inductors they hate changes in currents the quicker you try to change the current the more stronger emf they tend to induce and so one of their many applications is to maintain a steady current if you have some devices which are sensitive to current changes and you don't want them put an inductor in series with that it'll take care of it and we'll talk about more applications when we learn ac circuits