00:01
Yeah, we want to talk about some of the things that happen in an inductive circuit, both when you close the switch and let current flow through that inductor, and then what happens when you open the switch? so we're really going to think through, first of all, what if the switch has been closed for a very long time? and what we mean by that is the time is much greater than the time.
00:33
Time constant, which is l over r, time constant.
00:42
And we won't use any l or r here.
00:44
We'll just kind of write these schematically.
00:48
But in this case, so recall that how an inductor works is through faraday's law of induction, that that inductor fights change in magnetic flux through it.
01:05
And so there is a voltage across of it that's equal to, to, let's not call that e, i don't get it confused with the battery, but the voltage across the inductor is minus l, di by dt.
01:23
So if the circuit has been closed for a very long time with the switch, then there is no d .i.
01:34
By d .t.
01:35
We're in a steady state type situation.
01:38
And that means that the inductor acts like, a wire or a short if you want to think about it.
01:48
Inductor connects like a wire.
02:01
No voltage across it.
02:10
That means you basically have a circuit that looks like the battery in series with a resistor.
02:25
And the current is essentially equal to e over r.
02:32
Okay.
02:34
Now, if you were to open the switch suddenly, okay, so after s has been closed for a long time, if you open the switch, okay, all of a sudden you have a very large diy by dt.
03:00
Okay, now what governs the dt? we can write this as delta current over delta t.
03:09
The delta current basically is coming from the i initial, which is e over r, and it is trying to go to zero.
03:24
Delta t is governed by the time to disconnect the switch.
03:39
Okay, so there's a mechanism in there that we don't really know.
03:42
But this means that there is a huge voltage change, voltage vl across the inductor.
03:59
And it's going to be opposite what it was while the circuit was being charged up.
04:05
That is, the inductor will actually produce a positive voltage on one end towards the bottom and a negative v on the top.
04:20
In other words, the initial current was going in a direction basically clockwise through the circuit, and the inductor wants to maintain that.
04:35
It does not want to see a change in the current.
04:40
But depending on how quickly the circuit is disconnected, you could have a huge voltage difference.
04:50
And this means that if we look at the original circuit, okay, you have one end of the inductor, and let me draw the little switch in there, because that's going to become important.
05:13
You have one end of the inductor at a high negative potential, the other at a high positive.
05:22
And if you go back and look at the switch, it's got one of its ends at a very high, high negative potential and the other end at the battery voltage, which is not usually that high.
05:38
And so what can happen is there's a huge electric field between the ends of the switch...