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Current time:0:00Total duration:12:49

I want to talk about a new example of an inductor circuit and we have one shown here where this inductor is now controlled by a switch this is this is a push-button switch that we move in and out and this metal plate here will touch these two contacts and complete this circuit here this is a lot like the circuit we looked at before without the switch where the voltage source had a pulse going up and down this this circuit has a real interesting side effect when this switch opens up so let me give you a couple of examples for some practical examples of where this kind of an inductor will appear connect it to a voltage source and controlled by a switch and there's a couple of examples one of one of them is called a solenoid and a solenoid is a coil of wire that looks like this and has a as a metal rod going through it when you put a pulse of current into this what happens is the rod moves the rod will move back and forth so this is a way for instance a doorbell a doorbell is this kind of a actuator another kind of device that has an inductor in it or a coil is called a relay and that one again has a coil like this and these are all forms of an electromagnet and this one actually has a a switch some sort of a piece of metal that will move back and forth when the coil is energized this piece of metal will actually tip over here and when the current stopped it'll move back to its original state so for example if there's if there's a connection point here and a connection point here this piece of metal will go from making a short across there and move away and open and close this bigger switch so a relay is some sort of a switch and you might find this in a car where this relay is controlling like the windshield wipers of a car where the current for the windshield wiper goes through this switch and there's a smaller current over here that pulls the switch open and close to start and stop the windshield wipers or the motor and that's just two examples of where inductors or windings of wire can show up in in real applications and there's some fairly large currents that flow through these windings so we want to look what happens when we switch this current on and off and this is the example circuit that we'll use so we'll assume we have an inductor of 10 mil of Henry's and what we're going to do is we're going to push this push-button switch down and connect it up and then we're going to let it go and we're going to look at a couple of different voltages here this is going to be we'll call this voltage V and that's going to be measured with respect to ground and that is another voltage here that's interesting too which is VL and that's the voltage across the inductor so V Plus V L is equal to three volts all the time and now we look at what happens when we push the button down and then after that we'll look at what happens when we let go over the button something interesting is going to happen when we let go of this button so as we look at our circuit here we see there's an open circuit so there's no current flowing in here and that means I equals zero we'll call that i0 because it's the initial current when we could we closed our switch so now let's close our switch we'll do that like this and we just closed our switch at time T equals zero and let's look at what happens all of a sudden now our inductor has a voltage across it and it's a voltage of this node is at three volts this node is at zero volts so all of a sudden we have three volts across our inductor so let's use the integral form of the inductor equation to solve for the current that's going to happen here I equals one over L times the integral from zero to T of V D tau plus i0 let's fill in what we know I equals 1 over 10 mil of Henry's and V is a constant V is a constant 3 volts times 3 and it's the integral of D tau from zero to T and I 0 is 0 and then we get the final form which is I equals 3 over 10 mil of Henry's times the integral from 0 to t of d tau is just T and that's the answer so what we have here just like we did before when we had the the switching power supply just like we had before we were going to get a current that has a ramp that looks like that the slope of that is 3 over 10 million Riis which equals 300 amps per second so oh my goodness this current is going up really fast that's the slope of that current right there this is going up really fast and that's what it does now in a real circuit there'll be real resistances in here but it and so there'll be a limit to the amount of current that will be determined by the resistor but for the purposes of showing you just how this is this inductor equation works that's this kind of slope you would see at the initial closing of the switch okay I want to I'm going to clean off the screen here so I can keep my same circuit and now we're going to look at what happens here when we open this switch let me open the switch and now we've opened our switchback up it went that way all right so we have an initial current and it's sung is going to be some value depending on how long we held the switch down so it's going to be some current and that's flowing in the inductor now let's look at what happens when we open the switch and all of a sudden I goes directly and sharply to zero that's what the switch does when we open this switch contact one moment it's touching and the other moment is not touching so if we look at what's Delta I or what's di it's the ending current minus the starting current minus I and if we look at what's the time involved what's the change in time involved in opening a switch well it's something like zero the switch was closed then it was open and that's how much that take that took let's say that took zero time to happen now here's something that happens with inductors that is kind of strange let's calculate the voltage on the inductor right when this happens and we know that V equals L times di DT and plug in some numbers here so we have V equals L times what di is minus I over what over zero and that equals what that equals negative infinity what the heck is going on here is that possible no it's not well that's okay let's let's take a second let's say the switch didn't open in zero time let's say the switch let's say DT was let's say it was one nano second let's give us some time to open up all right that maybe that'll save us maybe that'll make more sense okay let's do that let's go V equals L times di DT and di we decided was minus I over it took one nanosecond to open the switch one nanosecond is one times ten to the minus nine okay so what is that equal to that equals L negative L times I times 10 to the holy cow 10 to the plus nine okay let's plug in some real values and see what we get here let's say let's say V equals let's say L was 10 mil of Henry's and let's say I was was 10 milliamps flowing down through the so Delta I is minus 10 milliamps and the time involved is 10 to the minus 9 seconds what does that work out to ten milli henries that's minus 3 and minus 3 so it's going to be 100 minus -3 minus 3 is minus 6 over minus 9 times 10 to the third okay that is and there's a minus sign here this says that V this point right here or the voltage across the inductor our calculation just said it's going to be a hundred minus a hundred thousand volts now minus a hundred thousand volts means that the negative terminal is a hundred thousand volts above the positive terminal so this voltage V is actually at a hundred and ten thousand volts how can this be this is a puzzle about inductors that we actually have to solve by actually looking right up close at what's going on here right in this switch area here so this is where reality comes in and saves us from our the crazy results we're getting from our ideal equations here so let's pretend here's here's the here's the the terminal of the switch right here let's do a blow up and here's here's that switch plate as soon as the switch moves away there's an air gap created here in our ideal world this air gap was a perfect insulator but what's going to happen because of these extreme numbers here because of this is happening this air gap is actually not an ideal conductor and what's going to happen is we're going to get a bright spark goes right across here this this really happens in real life there is actually when you open a switch there can be a little spark that goes between and that gives this equation here this di/dt enough time to release that energy and that current from the inductor continues to flow and go over into the switch that current will flow and it does it by breaking down air molecules and when you do that that voltage there for air if this gap here if this gap is one millimeter for air that's three thousand volts three thousand volts will cause that spark to happen there so this is what actually happens it and you can build switches that will take this spark and work for many years but it's not always a good idea to let this happen