Let's take a minute now and look at two variations of this simple RC circuit.

Now the one that we just analyzed, we'll look at that first.

Of course, the capacitor is over here. And we're measuring the voltage across

the capacitior. After I throw the switch closed.

And we know that it does this, it's starts off at 0 and then after a few RC

time constants, it reaches it's final value of V0.

Now we also saw that after one RC time constant, the voltage reaches about 63%.

Of the final voltage that it's going to achieve.

Now lets imagine that we start toggling this switch closed and open at some rate.

So, we can do it very rapidly or we can do it very slowly.

So now lets say first that we do it very rapidly.

Now what I mean by rapid is, so fast that the capacitor never has much of a chance

to charge up. So, that means rapid means on a time

scale that's short compared to the RC time constant.

So, if we're closing and opening this switch repeatedly, in a very rapid

fashion, then the voltage on the capacitor is never going to get very far

from 0. There just is not time for the capacitor

to charge up. I have to wait several time constants,

several RC time constants, for the capacitor to charge up.

So, of a rapidly changing signal, then, does not show up over here.

Now on the other hand, if I close and open the switch very slowly, and so the

time between successive openings and closings, let's say it's several RC time

constants long. Then the capacitor is going to reach the

battery voltage. And that signal is going to appear over

here. So, a slowly varying signal passes

through this circuit. A very rapidly changing signal does not.

And so for that reason, this kind of a RC circuit is called a Low Pass filter.

Now be careful of this, we're going to be making plots later on where this is

frequency on this axis, but in this case this is time.

And so the so when I say low pass, this is going to look opposite of the way this

looks when this is a frequency axis. But on time axis, when it's close to 0

here, then that is a Low Pass characteristic.

Now let's look at the other variation of this.

So, all I have to do is change the capacitor and the resistor, and now I'm

going to measure the voltage across the resistor.

Now, if you analyze this circuit, and I encourage you to work this out for

yourself, you're going to find a curve that is just the opposite of this one.

Or actually, of one minus this one. And so what happens in that case is that,

the voltage on the resistor is going to start off at the battery voltage, at the

instant I close the switch. And then as the capacitor charges up,