A question about basic parallel RC circuit

[ViolentCorpse]

In a series RC circuit, the current flows until the voltage of the capacitor equals that of the source so that the two voltages oppose each other and there's no net flow.

In a parallel circuit, the current indeed does stop flowing through the branch the capacitor is attached to (after the transients have died out of course), but for some reason my intuition (which is almost always wrong) tells me that the capacitor should prevent the voltage source from producing any current through the parallel resistor also, since there are only two nodes and on these nodes the capacitor and the source voltage should oppose each other, producing 0 current through the parallel resistor as well as through itself.

Mathematically, I think I understand why what really happens should happen, but I want a better physical understanding of it. I hope you get what I'm trying to say...

 

[milesyoung]

I'm not entirely sure I follow. If the capacitor is connected in parallel with the voltage source, why would it discharge when the voltage source is still present?

 

[ViolentCorpse]

I'm not exactly sure either. I think I had something else in mind. I'm very sorry. I'll edit my original post now.

 

[milesyoung]

There's certainly nothing to be sorry about. I was just trying to get you to expand a bit on what you meant.

 

[milesyoung]

I'd ask you to consider what happens in each branch after the voltage at the terminals of the capacitor equals that of the voltage source (which it will always do, by definition, for an ideal voltage source).

The capacitor and voltage source are at the same voltage, so the capacitor will draw no current, that much is true. The voltage of the resistor is also equal to that of the voltage source, so it must draw current in accordance with Ohm's law (V = I*R) - the voltage of the capacitor won't make any difference here.

Edit: Typo

 

[ViolentCorpse]

Thank you very much, milesyoung. I think I get it now. :)

 

[ViolentCorpse]

I have another question related to capacitors/inductors. I've learned that voltage across a capacitor and current through an inductor can not change instantaneously but I have seen many examples in my book where dvc/dt or diL/dt is non-zero. If an instantaneous change in these values is not possible, then why is their derivative not always zero?

 

[sophiecentaur]

I'm not too sure of what you are trying to say but you will always have resistive (Ohmic) components in any practical L or C and a structure of finite size will always radiate some power away, which represents a resistive component that will never be got rid of and resolves all those paradoxes about connecting capacitors together etc.

 

[milesyoung]

The voltage across a capacitor or the current through an inductor can not "jump" from one value to another, i.e. they must be continuous functions of time. If their derivatives with respect to time were always zero, this would mean they never change from their initial values.

 

[ViolentCorpse]

Ah, I see. Thanks again milesyoung and thank you sophiecentaur!