00:01
All right, so we're supposed to let this circuit go for a long time and then flip the switch.
00:06
And then we want to know some various quantities immediately afterwards.
00:14
I mean, the numbers are kind of ridiculous.
00:19
A three -farad capacitor is just, it would be an engineering marvel.
00:26
What we need to do, we first of all need to figure out what happens at long times before we flip the switch so we know have an idea what the currents are okay so here's the thing we let we have the switch open we're gonna let it go for a long time so there's two things that are going to happen at long times one is that the capacitor is going to charge because of the voltage source basically basically, we have an rc circuit here with r1 and c, never mind this stuff for right now.
01:07
But just think about this.
01:08
Remember, this is a linear operation.
01:11
So if we have, you know, we can talk about two sets of currents, one for charging the capacitor and the other that's kind of like a damped oscillation for this loop.
01:24
Okay and so for long times what happens is the damped oscillation over here because we've got resistor in series with inductor that oscillation is going to damp out to nothing over long times but the capacitor will be charged so so for t less than zero so we haven't flipped the switch yet here's what we we know i sub l is going to be zero and the charge on the capacitor is going to be related to the voltage of the source.
02:10
So it looks like that.
02:12
And i can actually multiply that out is 90 coulombs.
02:19
And these numbers are really kind of ridiculous, but nonetheless.
02:27
So those are our initial conditions.
02:30
And by the way, ir equals ic equals zero.
02:35
So these are the initial conditions for t greater than zero.
02:40
Okay.
02:43
So here's what we know.
02:45
The current in the inductor is still going to be zero because that's the initial condition that really matters.
02:54
That whatever current we had in the inductor is going to be the same when we go to that short time.
03:08
Okay, so il is still going to be zero.
03:14
And the charge on the capacitor doesn't change instantaneously either.
03:20
So for t greater than zero, the capacitor is still going to have this amount of charge.
03:28
So let's draw our circuit and think about this a minute.
03:31
It.
03:32
So here's our circuit diagram and we're interested in t equals zero plus so just after t equals zero.
03:44
All right so here's what we got.
03:46
So we know the current in the inductor is zero.
03:51
Okay so we can kind of forget about that branch.
03:55
As far as the capacitor goes it's charged and so so it acts like a battery for that instant right after the switch is closed.
04:08
After that, the charge does something else.
04:13
But for that split second right after the switch is closed, the capacitor acts like a battery.
04:25
Okay.
04:43
All right.
04:44
So the initial voltage on the capacitor is 30 volts because it's charged, right? right.
04:49
And so i'm going to draw this circuit like this.
04:55
I'm going to ignore the inductor and i'm going to replace the capacitor with a battery...