Why does current initially rush into a capacitor?

In summary: Yes, the electric field will oppose the change in voltage across the capacitor, leading to a more gradual current flow.
  • #1
TimNJ
21
1
Hi all,

I'm trying to wrap my head around the physics behind the current that initial flows when a voltage step is applied across a capacitor. Namely, why does a large current initially flow into a parallel plate capacitor, but a large initial current does not flow if the capacitor is replaced by two simple wires (left unconnected)?

I understand that when a voltage is applied across any device, charges will redistribute (rapidly) such that the voltage across the device becomes equal to the voltage of the source.

So, what's so special about a capacitor (two metal plates close to each other) that causes this initial redistribution of charge to require such a large initial current?

Thanks!
Tim
 

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  • #2
Nothing special about the plate configuration as far as that initial current. It's an uncharged conductor connected to a source of charges. Therefore the charges will move in such a way to try to equalize the potential. Same as touching any charged conductor to any uncharged conductor.

And when conductivity is high, as in a metal, that means the charges can flow quickly as they equalize, leading to a large current.

TimNJ said:
but a large initial current does not flow if the capacitor is replaced by two simple wires (left unconnected)?

Wires can be considered as a capacitance also. In fact the capacitance of wires can lead to some problems in some circuits. But it's a very small capacitance and it reaches potential V when only a small amount of charge has moved. A parallel plate capacitor is designed for charge storage, designed to require more charge before it reaches V.
 
  • #3
If the capacitor were not there and you merely had the ends of two wires, there would still be a potential difference across the gap and hence some charge accumulation of positive and negative charges at each end. It's just that the amount of charge would be small because the capacitance would be low. The two metal plates have a larger capacitance, i.e. are an arrangement that stores more charge for the same voltage than the ends of the wires.
 
  • #4
Thanks RPinPA. I guess that's why the peak current is simply V/R? So with normal conductors, there is a high initial current, but it is so brief that we don't even worry about it in most analysis?

In a capacitor, charge continues to flow until the voltage reaches equilibrium?
 
  • #5
TimNJ said:
Thanks RPinPA. I guess that's why the peak current is simply V/R? So with normal conductors, there is a high initial current, but it is so brief that we don't even worry about it in most analysis?

Yes. I typed an update while you were responding.

TimNJ said:
In a capacitor, charge continues to flow until the voltage reaches equilibrium?

Yes, because that's what a conductor does, and capacitors are made of conductors. What the parallel plate configuration does is lower the potential by the nearby presence of opposite charges, thus requiring more Q to reach a given V.
 
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  • #6
TimNJ said:
In a capacitor, charge continues to flow until the voltage reaches equilibrium?
Another way to look at it is that when the capacitor is initially uncharged, the voltage across its plates is zero therefore the voltage across the resistor is equal to the battery voltage but only initially. Current will flow through the resistor according to Ohm's law and will start accumulating on the plates with electrons moving from the negative plate to the positive. The charge accumulation on the capacitor reduces the voltage across the resistor which in turn reduces the current through it. When the voltage across capacitor matches the battery voltage, the current through the resistor goes to zero, i.e. there is no more current in the circuit. All this can be summarized with the following statement: "If an uncharged capacitor is connected to a battery through a resistor, it will behave as a straight wire (short circuit) immediately after and as an open switch (open circuit) a long time later. What constitutes "long time" depends on the time constant ##RC##.
 
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  • #7
"Why does current initially rush into a capacitor?"
With a large series resistor there is no "rushing". Charge can just be leaking very slowly - and getting slower and sslloowweerrr.
 
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  • #8
RPinPA said:
Yes. I typed an update while you were responding.

Thanks. I like thinking of it that way, I think. Here's what I take from that: If the source voltage is changed, then there will be a transient state, during which charge redistributes and voltages reach equilibrium. Even if there are just two unconnected wires hanging off a step-voltage source, there will be a extremely brief instantaneous "current", caused by electric field propagation down the line. In this situation, the change in voltage on a conductor is basically unopposed.

However, when you put a parallel plate capacitor at the end of those wires, the change in voltage across the capacitor is opposed by the electric field setup between the plates of the capacitor. The instant charge begins to flow into a capacitor, an opposite amount of charge flows out of the opposite plate, causing a charge imbalance, and thus electric field.

This electric field has an attractive force which "pulls" more charge onto the plate. More charge continues to flow into the capacitor until the electric field caused by an accumulation of like charges equals the electric field setup between the two plates.

Does this sound correct?

Thanks!
 
  • #9
kuruman said:
Another way to look at it is that when the capacitor is initially uncharged, the voltage across its plates is zero therefore the voltage across the resistor is equal to the battery voltage but only initially. Current will flow through the resistor according to Ohm's law and will start accumulating on the plates with electrons moving from the negative plate to the positive. The charge accumulation on the capacitor reduces the voltage across the resistor which in turn reduces the current through it. When the voltage across capacitor matches the battery voltage, the current through the resistor goes to zero, i.e. there is no more current in the circuit. All this can be summarized with the following statement: "If an uncharged capacitor is connected to a battery through a resistor, it will behave as a straight wire (short circuit) immediately after and as an open switch (open circuit) a long time later. What constitutes "long time" depends on the time constant ##RC##.

Yes! From a circuit analysis perspective that certainly checks out! Thank you for that.
 
  • #10
TimNJ said:
This electric field has an attractive force which "pulls" more charge onto the plate.
Ignoring any relative potential between the circuit and Earth, there is a 'pull' on the electrons from one plate (+) and a 'push' from the other (-). The same magnitude of charge collects on each plate; no total charge is gained or lost.
 
  • #11
sophiecentaur said:
Ignoring any relative potential between the circuit and Earth, there is a 'pull' on the electrons from one plate (+) and a 'push' from the other (-). The same magnitude of charge collects on each plate; no total charge is gained or lost.

That makes a lot of sense. Thanks.

I guess I still have some confusion with respect to the different electric fields, specifically how they change with time, and how that relates to the charging behavior of capacitor. I've ordered an old edition of a book "Matter & Interactions" by Sherwood and Chabay, that I hope will have some answers to my conceptual misunderstandings.
 

1. Why does current initially rush into a capacitor?

Current initially rushes into a capacitor because of the difference in potential between the two plates of the capacitor. When a voltage is applied across the capacitor, the electrons on one plate are repelled and the electrons on the other plate are attracted. This creates a flow of current from the source to the capacitor, filling it up with electrons.

2. How does a capacitor store charge?

A capacitor stores charge by creating an electric field between its two plates. When a voltage is applied, the electrons on one plate are pushed away from the other plate, creating a separation of charge. This stored charge can then be released when the capacitor is connected to a circuit.

3. What happens to the current after it rushes into a capacitor?

After current rushes into a capacitor, it starts to decrease as the capacitor becomes charged. This is because the capacitor acts as an open circuit once it is fully charged, preventing any further flow of current. However, the capacitor can release its stored charge when connected to a circuit, creating a brief surge of current.

4. Why does current eventually stop flowing into a capacitor?

Current eventually stops flowing into a capacitor because the capacitor becomes fully charged. Once the potential difference between the plates of the capacitor is equal to the applied voltage, the capacitor acts as an open circuit and no current can flow through it. This is known as the steady state condition.

5. Can a capacitor store an unlimited amount of charge?

No, a capacitor has a maximum amount of charge it can store, known as its capacitance. The capacitance of a capacitor is determined by its physical properties, such as the distance between the plates and the type of dielectric material used. Once the capacitor reaches its maximum charge, any additional current will cause it to breakdown and potentially fail.

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