# Case of a charged capacitor

It is given that an uncharged capacitor is connected with a battery. Clearly, it gets quickly charged and flow of current stops in the circuit. What is the reason behind a charged capacitor in completely restricting the flow of current ?

phyzguy
A capacitor is two conductors separated by an insulator. In the DC case, there is no path for the current to flow across the insulator.

A capacitor is two conductors separated by an insulator. In the DC case, there is no path for the current to flow across the insulator.
But while charging, doesn't current flow in the circuit?

phyzguy
But while charging, doesn't current flow in the circuit?

Yes, but the situation is a little bit subtle. When the capacitor is charging, a current I is flowing into one side of the capacitor, and the same current I is flowing out the other side. So, from the outside, it looks like a current I is flowing through the capacitor. But that isn't what is happening. The current I flowing into one side is being stored as charge on one capacitor plate, and a current I is leaving the other capacitor plate causing it to build up an opposite charge. So in no case does current flow across the insulating gap between the two conductors. Do you see?

• davenn
Yes, but the situation is a little bit subtle. When the capacitor is charging, a current I is flowing into one side of the capacitor, and the same current I is flowing out the other side. So, from the outside, it looks like a current I is flowing through the capacitor. But that isn't what is happening. The current I flowing into one side is being stored as charge on one capacitor plate, and a current I is leaving the other capacitor plate causing it to build up an opposite charge. So in no case does current flow across the insulating gap between the two conductors. Do you see?
Of course that's true but then how would you explain the flow of current through a circuit as a whole then? In the charged cased, current doesn't flow in the circuit and of course,not between the capacitor plates. While charging, current flows through the circuit but not between the capacitor plates. But as such, how does a capacitor simply block the flow of current when completely charged? And how does current flow through the entire circuit while charging as there is a insulating medium in the path of the current (in the capacitor) ?

phyzguy
And how does current flow through the entire circuit while charging as there is a insulating medium in the path of the current (in the capacitor) ?

I thought I explained this. Read my explanation again. If I consider the capacitor as a "black box" and only look at the wires going in and out, there is a current I flowing in to one wire, and a current I flowing out of the other wire. So it looks like current is flowing through the "black box". You have no way of telling that the current is actually stopping when it hits the insulator and starting up again on the other side.

Lord Jestocost
Gold Member
While charging, current flows through the circuit but not between the capacitor plates.

There is no conduction current flowing between the capacitor plates because there aren't - in the ideal case - mobile charged carriers. However, as long as the charging progresses, there "flows" - so to speak - a displacement current inside the capacitor which is related to the temporal change of the electric field between the capacitor plates.

There is no conduction current flowing between the capacitor plates because there aren't - in the ideal case - mobile charged carriers. However, as long as the charging progresses, there "flows" - so to speak - a displacement current inside the capacitor which is related to the temporal change of the electric field between the capacitor plates.
Yes but my doubt is exactly how does current flow through the circuit when a capacitor is connected to it ? Current flows through the external circuit, but when I consider the capacitor charge accumulation takes place on the respective plates simultaneously. I am unclear with the idea of the capacitor allowing no current to pass when both the plates of the capacitor have maximum charge accumulated on them.

phyzguy
Yes but my doubt is exactly how does current flow through the circuit when a capacitor is connected to it ? Current flows through the external circuit, but when I consider the capacitor charge accumulation takes place on the respective plates simultaneously. I am unclear with the idea of the capacitor allowing no current to pass when both the plates of the capacitor have maximum charge accumulated on them.

I don't know how to explain any more clearly. What about my explanation do you not understand or disagree with?

I don't know how to explain any more clearly. What about my explanation do you not understand or disagree with?
I don't find the explanation in sync with the doubt that I have. :(

phyzguy
I don't find the explanation in sync with the doubt that I have. :(

Can you state your doubt more clearly? If your question is "How does current flow across the dielectric cap?", then the answer is either:

(1) It doesn't. It stops at the dielectric gap and new current starts on the other side of the gap.

(2) The physical current is converted to a displacement current and the displacement current flows across the gap.

• davenn
I am unclear with the idea of the capacitor allowing no current to pass when both the plates of the capacitor have maximum charge accumulated on them.
This is my doubt.

Can you state your doubt more clearly? If your question is "How does current flow across the dielectric cap?", then the answer is either:

(1) It doesn't. It stops at the dielectric gap and new current starts on the other side of the gap.

(2) The physical current is converted to a displacement current and the displacement current flows across the gap.
Lets put it this way, obviously current flows in the circuit and till that time there is a varying electric field inside the capacitor. Now I am not sure why does the flow of current stop when the electric field becomes constant inside the capacitor.

Dale
Mentor
2020 Award
Have you been introduced to the concept of the “displacement current”?

phyzguy
Current only flows into (or through) the capacitor when the voltage is changing. When the voltage is constant, then the charge on the capacitor doesn't change, so the current (which is dQ/dt) is zero. This is why the current through a capacitor is given by I = C dV/dt.

Have you been introduced to the concept of the “displacement current”?
I think I'm a bit hazy about it.

Current only flows into (or through) the capacitor when the voltage is changing. When the voltage is constant, then the charge on the capacitor doesn't change, so the current (which is dQ/dt) is zero. This is why the current through a capacitor is given by I = C dV/dt.
Ok, thanks a lot.

phyzguy
Lets put it this way, obviously current flows in the circuit and till that time there is a varying electric field inside the capacitor. Now I am not sure why does the flow of current stop when the electric field becomes constant inside the capacitor.

The current stops because the voltage stops changing. Since I = c dV/dt, I = 0 when V is constant.

• ubergewehr273
phyzguy
Ok, thanks a lot.

davenn
Gold Member
Case a of a charged capacitor.

Ohhh and capacitors are NOT CHARGED

Capacitors are energised. The capacitor that has 1000V across it has the same charge as a capacitor that has 0V across it = 0 ( zero)
that is, the net charge on a capacitor is zero.
For every negative charge on one plate, there is an equal number of positive charges on the other plate

Dave