00:01
We have this circuit that we're going to let run for a long time with the switch in the left position.
00:10
So they've thrown a curveball at us by making v1 be minus 5 volts, but that's okay.
00:19
We can deal with it.
00:21
But some of the answers are going to look a little weird because of it.
00:26
It.
00:26
So we put it in the left -hand position for a long time.
00:31
And then what's going to happen is the capacitor is going to charge and then the current will be zero.
00:40
That's because of long times.
00:43
There's no current in the capacitor at long times.
00:46
So the charge on the capacitor, capacitor which will be our initial charge is going to be minus cv because the reason it's negative well let's write it as cv but then remember that v is negative so we got one millifarad times minus five volts so that's minus five millicoulombs which means that at t equals zero in fact the charge on the top plate is negative and the charge on the bottom plate is positive then we're gonna flip that switch over okay and then our we flip the switch at t equals zero so the equation we get looks like this it's the same one we would always get for a circuit with a capacitor and resistor which is what they call v5.
02:36
I don't know how they're not why they're not i don't know why they're numbering seems very weird this is v5.
02:53
So the equation still looks the same this should be dq dt then our current by the way is going in this direction all right and we know what the the solution to that looks like.
03:36
Let's write it out with the numbers.
03:39
So we got, all right, so here's the form of our solution.
04:22
Go back to the start.
04:25
Here's our differential equation.
04:27
Here's the form of the solution...