 This video is just going to be a walkthrough of what happens to the current in this circuit here as it flows through and What this inductor does to it what this happens to this resistor? We're going to work out volt drops across the inductor volt drops across the resistor We're going to work out the energy stored in this inductor. I'm assuming that you understand how the circuit works This is more of a walkthrough of how the math works Now just as a quick little refresher when we have this circuit Let's just quickly draw this in here. This will be my current. This will be my time the moment I close this switch right here current starts at zero and Then it starts to climb so we start here and it starts to climb until it reaches a steady state Now it takes five time constants to get there one two three four five Till it reaches steady state, so we're going to walk through that assuming you know this So let's take a look at throwing some values at this Now here I've got some values. I've given the battery 200 volts I've given the inductor 300 millihenries, and I've given the resistor 15 ohms Anybody notice now I've closed this switch So we're going to walk through the math of all this We're going to see what happens to the current as it rises up through this whole circuit We're going to see a volt drops across this guy and a volt drop across this guy, and we'll talk about the energy stored So here we are I've kind of shrunk it down a bit. These are the things that we're going to be working out We're going to work out ISS, which is current at the steady state. That's right here Then we're going to work out. This is current at the first time constant or first tau Then we're going to also work out the voltage at the first tau of the resistor. That's this voltage here at the first Oh, then we're also going to talk about the voltage at the inductor because there's going to be a volt drop there as Well, and then at the end of it we're going to talk about the w which is the energy stored in this guy After current is up and running Now let's quickly look at a refresher of the formulas that we need to know for this So here the formulas we're looking at let's start out with our tau. That's our time constant Remember I talked about how it takes five time constants to reach our steady-state current So what we do is we work this out by taking this guy tau is equal to your inductor or your inductance Sorry divided by your resistance and that gives you one tau and we have to remember that it takes five Let me just redo that. That's a terrible five five tau To steady-state So that's we got to remember that whatever number that we work out here We have to multiply that by five to get to our steady-state current Our next formula. Let's just get rid of this guy here is your current at the tau So this is your eye at tau So if I wanted to work out what my current was at any particular time constant I use this formula, which is in another video. I showed you how to do this One minus e to the negative x times your steady-state current will give you your current at that tau Remember this is that napier's constant that negative x. That's your time constant So if you're working it out at the first time constant, it's negative one second time constant negative two third time constant negative three fourth time constant negative four fifth time constant negative five sixth time constant Just kidding. There's no sixth time constant So and this one here that stays the same no matter what I don't care what time constant you're in it's always one there Then just to talk about the voltage at the resistor at a certain time constant We just take this current that we worked out at that time constant using ohm's law We multiply that by the R and we get the voltage at the resistor Then as a quick aside here the voltage at the inductor v of L at that tau We can't use current across the inductor that doesn't give us the voltage So what we have to do is work out what the voltage of the resistor is then we malt the sorry not multiply it We subtract it from the source voltage and that is the voltage at the inductor because Kirchhoff's law has to apply and Then we have this the w or the wubble you as That German boss of mine would used to call it and that is just point five times the inductance times the steady-state current squared Those are the formulas that we're gonna be using in the next little bit. So let's take a look at the problem get cracking on it When working these problems out the first thing we've got to figure out is our ISS or steady-state current Remember that inductance is the property of an electrical circuit that opposes any change in Current so everything is based off of that ISS. So let's work that out right now. I've got 200 volts right here. I've got 15 ohms that ends up equaling 13.33 amps. Let's write that in here 13 point Three amps. So that's going to be our steady-state current. That's what we're starting out with Now what we're going to do is we're going to work out what our current is at the first tau So that's this guy right here now in order to do that. We are going to be using the formula again one minus e to the negative one times I s s So I'm going to plug that into my calculator and I'm going to get that current and that current works out to be 8.4 amps 8 point four amps and That's that current at the first tau Now to walk this through and this should make more sense now if I've got 8.4 amps Right flowing through the circuit. That means I've got 8.4 amps going across this 15 ohm resistor So in order to get this resistance, I just go 8.4 amps times 15 ohms and that will give me my voltage at the first tau that works out to be 126 volts 126 volts So we're on our way We have now figured out what the current is at the first tau We figured out what the voltage of the resistor is at the first tau Now we need to figure out what the voltage at the inductor is at the first tau in order to do that We know that we have 200 volts Let's just kind of call attention to that so I got 200 volts right there and at this point I have 126 volts across this guy so in order to get this using Kirchhoff's law 200 minus 126 volts gives me 74 volts So I've got 74 volts across my inductor So it's that it doesn't matter which we're using if you're using say I wanted to figure out what the Voltage was at the second tau I'd work out what my current is going through here at the second tau Then I would multiply that current times this resistance to figure out what the resistive voltage is at the second tau Then I would take my source voltage minus that voltage to get this voltage It's usually the trickiest part of these things, but it doesn't have to be that hard as you can see The last thing here is we've got to figure out how much energy is being stored in those magnetic lines of flux that surround this Inductor in order to do that. We just take that formula w is equal to 0.5 li squared w is equal to 0.5 li squared We do that and we punch those numbers in and we get 26.5 Joules, let's get that written up there 26.5 Joules of energy stored in the magnetic lines of flux surrounding this inductor and that is a complete walk-through I use it at the first how you could use it at the second third fourth fifth how It doesn't matter as long as you're using this formula this e to the negative x. So let me just Rate that up here because that's I've got it written down for the first time, but it's 1 minus e to the negative negative x times I s s that formula there unlocks everything now just as a side x for some reason get a couple dots there That's supposed to be a minus x this x again is your time constant first time constant negative 1 second time constant negative 2 and so on and so on That's it. That's the walkthrough