[Coda]

Originally Posted by Potironette

For parallel circuits, can I also pretend that all the resistors in parallel merge together into one resistor?

In terms of how the rest of the circuit sees it? Yes.

(I think based on what I learned in class today, I am treating parallel circuits that way. As for the equation, I do remember how to find it, though I wonder why that's the equation on my reference sheet and not (R_1 * R_2)/(R_1 + R_2) = R_eq )

Because they're equivalent (it's pretty simple manipulation to prove it), and 1/R_eq = 1/R₁ + 1/R₂ is less work to evaluate. :P

Err..so voltage measures change in potential energy based on current and time, and when voltage drops it means some potential energy got converted into some other energy across a resistor?

That's one way to look at it, yes.

And all the while the battery has its own voltage, potential isn't the only thing that matters...so resulting from the potential is electrons moving--which is kinetic energy. But, just like how if I slide a book across the table, the kinetic energy of the book is lost to friction/heat/etc. and it stops, the electrons are sort of "stopping"--except there is a constant "force." Therefore, just as pushing a book across a table vs across a rug, more KE is lost to heat across the rug and so it is slower, so too does more resistance mean the current is slower across a circuit with more resistance?

Precisely.

And is that why Power = Work/time = ΔPE/time? Because somehow, change in PE is sort of Force (and distance)...P = W/t --> W = Fd = ΔPE for electric fields = qEd = qΔV --> P = qΔV/t --> P = VI?

Looks like you've basically got it down.

Why doesn't distance matter in a circuit? Does it really just not exist as a value? But at the same time, I can't very well say P = F/t, because then P = IE.

Distance doesn't matter in a circuit for the same reason that current is constant across a circuit: it doesn't matter how far the other end of the wire is, when you push on the electrons on the near end, it forces electrons out on the other end. While the individual electrons don't move very fast, the energy propagates through the wire at an appreciable fraction of the speed of light, so you can more or less disregard it at human scales.

EDIT: Random question-how does a voltmeter measure voltage? I assumed that the greater the current passing through the voltmeter, the greater the voltage measured. But apparently the ideal voltmeter has infinite resistance? Doesn't that mean no current passes through the voltmeter? And if there is no current, how does it measure anything?

The ideal voltmeter has infinite resistance so that it doesn't interfere with the circuit being measured by using up some of the current. (After all, by applying a voltmeter to a circuit, you're creating a parallel circuit!) The conflict you're trying to resolve HAS no resolution because an ideal voltmeter is impossible. :P You're completely correct: it HAS to have SOME current flowing through it in order to measure anything. From that point, it's just V=IR, and you know the resistance of the voltmeter and you measure the current flow so you can determine the voltage.