How do capacitors act in zero-resistance circuits?

[Medicore123]

Assuming you had a power supply, a switch and a capacitor in series (no resistor and the wires/power supply have no resistance), would the capacitor charge instantaneously when you closed the switch (because the P.D. across the capacitor would become equal to the P.D. of the supply right away, I think)? The time constant, as far as I'm aware, would be = 0 seconds for this case. What would then happen if the switch was opened?

NOTE: by 'instantaneous', I mean the rate of charge/discharge is only limited by the speed at which electric fields can propagate through space etc.

[John Cuthber]

Even without any resistance, the circuit would have inductance and that would limit the rate at which the charge on the capacitor could change.

[Medicore123]

Please could you briefly elaborate about how the inductance limits the charging rate?

[studiot]

http://www.eeweb.com/toolbox/wire-inductance

[John Cuthber]

The initial current is zero.

The rate at which that current can change is limited by the inductance and the voltage

DI/Dt = V/L.

 

 

If the time constant was zero, the initial current would have to be infinite (so the capacitor can gain a charge equal to CV in zero time.

But that would mean that it had changed from zero to infinity in a very short time (ideally zero time).

That would require either an infinite voltage or a zero inductance.

 

Neither of those is going to happen.

So the time constant can't be zero.

[Medicore123]

Thanks!

[Delbert]

To cause anything to change from zero to an infinitely fast or large state of movement requires an infinite amount of energy.

 

The current in your hypothesis of a circuit of zero resistance will be limited by inductance, not forgetting opposing eddy currents within the body of the conductor. And opposing eddy currents within the body of a conductor I understand is referred to as skin effect. Which means high frequency currents, or any fast changing current as in your case, will be limited to flowing close to the surface of the conductor. And the faster the change in current, the thinner the layer of conduction. And the infinitely fast rate of change of current in your hypothesis would presumably mean an infinitely thin layer of conduction - the conclusion being that such a infinitely thin layer will present a high resistance even in a zero resistance conductor!