# If current doesn't flow in an open circuit, how are capacitors charged?

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1. May 2, 2015

### x86

When answering a related question on physics forum, I found something I seemed to be confused about:

Suppose we have a battery connected in series to a capacitor with no charge. A capacitor with no charge on it acts like an open circuit.

I know what happens next: the battery charges the capacitor until the potential difference between the battery and capacitor are equal.

But I'm confused about what happens inbetween. If the capacitor acts like an open circuit when it has no charge, then how does current from the battery flow in the first place so that it can charge the capacitor?

Last edited: May 2, 2015
2. May 2, 2015

### Staff: Mentor

A capacitor acts like an open circuit to DC, not to AC. The charging process is a changing current, so it's an AC situation. Once fully charged with a DC voltage across it, the capacitor looks like an open circuit with no current flowing.

Are you familiar with the concepts of "impedance" of inductors and capacitors? Have you seen the differential equations relating voltages and currents for inductors and capacitors?

3. May 2, 2015

### x86

Yes, I am familiar with impedance. I've also seen differential equations (only first order) for inductors and capacitors.

And yes, that makes sense now. I remember hearing something about capacitors being short circuits leaving the transient stage, and inductors being open circuits.

So I guess that makes sense now.

4. May 3, 2015

### jim hardy

We get accustomed to thinking steady state and forget our basics. Well, i do anyhow ..

A discharged capacitor has no voltage across its dielectric .
So there's no energy stored in that dielectric.

We can "charge" the capacitor by pushing some charges onto one plate and pulling some off the other plate.
The first few charges are quite easy to move because there's no electric field opposing their movement.

As we move more of them, the electric field between the plates becomes more intense. So it pulls at the charges we're removing from one plate and pushes against the charges we're adding to the other plate.

Observe the total charge in the capacitor doesn't change - the charge added to one plate is equal to the charge removed from the other plate.
Yet we say that a capacitor "stores charge" ?
Really, it stores energy. One of those quirks of language...
The force to push charge onto one plate and pull it off the other represents work and that work is stored as potential energy in the E-field inside the dielectric between the plates.

Now , we know that the rate of electron drift is slow. So the charge we get out one end of any device, even a simple wire, is not the same exact one that entered the other end, but it's identical so we say that charge propagates "through" the device.

Here's the key point - Charge gives up energy on its way through a device. That energy goes into the E-field in the dielectric of a capacitor, or into the magnetic field surrounding an inductor, or into the internal heat content of a resistor.

Those first few charges "through" a capacitor sneak through against such a weak E-field that there's almost no energy given up to that field, which means almost zero zero voltage drop , and that's the way to remember why a discharged capacitor is almost a short circuit. Almost zero volts implies almost a short circuit.

Simple mental pictures like above help me arrive at the correct formulas.
This E-field that's linear with charge yields a formula exactly like the one for a linear spring where force is linear with displacement:
F=KX is analogous to Q=CV
and
W=½KX2 is analogous to W=½CV2

Of course springs, capacitors and inductors which store energy can also return it, so adjust my word picture above to make it bidirectional for those devices.

http://amasci.com/emotor/cap1.html

regards

old jim

Last edited: May 3, 2015
5. May 3, 2015

### jim hardy

thanks mentor for correcting my mistake yesterday
thanks x86 and dave for the feedback

old jim

6. May 3, 2015

### meBigGuy

How does a radio antenna receive radio waves? How does a moving magnet cause current to flow in a wire? Changing Electromagnetic fields cause currents to flow ( and are produced by changing currents). Roughly speaking (cause/effect can be difficult to separate sometimes) , the electromagnetic field that gets set up between the plates of a capacitor causes currents while it is changing.

7. May 3, 2015

### Delta²

Well though there is no electric charge flowing between the plates of the capacitor, there is the infamous displacement current, that is a "virtual" current that corresponds to the rate of change of electric field between the plates of the capacitors as the capacitor is charging.

Ofcourse it turns out that it isnt virtual at all in the sense that a time-changing electric field creates a (time-changing) magnetic field, pretty much the same way as an ordinary current (that is a flow of electric charges) creates a (changing) magnetic field. The displacement current is included in the Maxwell-Ampere equation, that is the most general equation that describes (together with the other 3 Maxwell's Equations) all electric and electromagnetic phenomena.

So yes dont get confused but a capacitor creates a magnetic field also, due to the displacement current.

Last edited: May 3, 2015
8. May 4, 2015

### jim hardy

Seems to me it gets right down to the fundamental question "what is the nature of space and why is it so intertwined with electomagnetics?"

i need an aether......

old jim

9. May 4, 2015

### Scommstech

I was always taught that it was "displacement current". In a capacitor there was no actual movement of free electrons from one atom to another as in normal current flow but the capacitors insulating dielectric layer 's electrons were forced by the EMF applied to "displace" towards or away from the applied force, becoming known as the charge.. This applies equally to DC as AC. The difference was that AC energy was detected on the far plate to the applied force and could influence a conductor attached causing it to displace its own electrons, resulting in current flow. If the applied force exceeds the insulating properties then electrons can be "torn" out of their atom hold and the capacitor's insulation breaks down. A healthy capacitor will hold its charge if removed from the applied force.
Regards

10. May 4, 2015

### sophiecentaur

You say aether, I say either?

11. May 4, 2015

### DrZoidberg

12. May 4, 2015

### meBigGuy

Great lectures.

13. May 5, 2015

### Delta²

I guess you are joking but displacement current isnt known to the wide public(like the ordinary current is) but it is well known among anyone who studies electromagnetism in depth. Many books commit a whole chapter for it and how the genius of J.C. Maxwell conceive it and add the term to the Ampere's law, which led to the theoretical discovery of electromagnetic waves in vacuum that travel with the speed of light.

Electromagnetism is the magic of this universe, it is the connecting link between microscopic and macroscopic phenomena and processes, while nuclear (strong and weak) field has only to do with the microscopic world and gravitational field only with the macroscopic phenomena

Last edited: May 5, 2015
14. May 6, 2015

### jim hardy

no, i was speaking truthfully.
My electrodynamics is weak. I spent a lifetime working with circuits and machinery where the energy is constrained to wires, and the cores of transformers and motors.

I appreciate your sharing the concepts.
I just bookmarked this link
http://www.maxwells-equations.com/
high time i became more fluent.

old jim

15. May 6, 2015