I asked a relatively simple question. Unfortunately, the answers provoke far more questions! :-(
It seems that I don't actually understand RC circuits at all. In particular, why there's an R in there. It seems completely unnecessary. Surely the capacitor is doing all the work? What the heck do you need a resistor for?
Clearly my mental model of how this stuff works is incorrect somehow. So let me try to explain my mental model:
If you try to pass a direct current through a capacitor, you are just charging the two plates. Current will continue to flow until the capacitor is fully charged, at which point no further current can flow. At this point, the two ends of the wire might as well not even be connected.
Until, that is, you reverse the direction of the current. Now current can flow while the capacitor discharges, and continues to flow while the capacitor recharges in the opposite polarity. But after that, once again the capacitor becomes fully charged, and no further current can flow.
It seems to me that if you pass an alternating current through a capacitor, one of two things will happen. If the wave period is longer than the time to fully charge the capacitor, the capacitor will spend most of the time fully charged, and hence most of the current will be blocked. But if the wave period is shorter, the capacitor will never reach a fully-charged state, and most of the current will get through.
By this logic, a single capacitor on its own is a perfectly good high-pass filter.
So... why does everybody insist that you have to have a resistor as well to make a functioning filter? What am I missing?
Consider, for example, this circuit from Wikipedia:
What the hell is that resistor doing there? Surely all that does is short-circuit all the power, such that no current reaches the other side at all.
Next consider this:
This is a little strange. A capacitor in parallel? Well... I suppose if you believe that a capacitor blocks DC and passes AC, that would mean that at high frequencies, the capacitor shorts-out the circuit, preventing any power getting through, while at low frequencies the capacitor behaves as if it's not there. So this would be a low-pass filter. Still doesn't explain the random resistor through, uselessly blocking nearly all the power on that rail...
Obviously the people who actually design this stuff know something that I don't! Can anyone enlighten me? I tried the Wikipedia article on RC circuits, but it just talks about a bunch of Laplace transform stuff. It's neat that you can do that, I'm trying to understand the underlying physics. And failing!
(Similar arguments to the above suggest that an inductor by itself ought to make a good low-pass filter — but again, all the literature seems to disagree with me. I don't know whether that's worthy of a separate question or not.)