# How does current flow in a circuit with a capacitor?

When a capacitor is connected to a battery, current starts flowing in a circuit which charges the capacitor until the voltage between plates becomes equal to the voltage of the battery.

Since between plates of a capacitor there is an insulator/dielectric, how is it possible that current flows in a circuit with a capacitor since according to Ohm's law, current is inversely proportional to resistance and an insulator by definition has a big resistance, so we basically have an open circuit?

Since this is a physics q and a, a physics explanation is in order.

There are two kinds of current.

Conduction current is a net flow of charges. It is was people usually think of when the word "current" is used

Displacement current is another form of current, first recognized by Maxwell. Displacement current plays an essential role in Maxwell's equations. Displacement current density is proportional to the time derivative of the change of electric flux density.

When electron current flows into one side of a capacitor, the electrons accumulate, as there is no place for them to go. As the electrons accumulate, the electric flux density changes. This causes, or perhaps "is" a displacement current.

On the opposite plate of the capacitor, a similar process occurs, but with opposite electrical polarity.

The displacement current flows from one plate to the other, through the dielectric whenever current flows into or out of the capacitor plates and has the exact same magnitude as the current flowing through the capacitor's terminals.

One might guess that this displacement current has no real effects other than to "conserve" current. However, displacement current creates magnetic fields just as conduction current does.

This answer is perhaps more than one might want to know, but it is part of the story of electricity that is worth telling.

• Yes. Thank you. Displacement current just refers to the fact that electric field changes in time as capacitor is being charged which has an effect of creating a magnetic field according to Ampere's law just like a real current does. I was kind of confused on this question since I know when circuits are opened, current doesn't flow. When we have an open circuit, which is basically in simplest scenario two unconnected conductors placed in air (capacitor), capacitance of such a capacitor is so small that voltage of battery charges it so quickly that current very fastly stops flowing. – Dario Mirić Jun 12 at 7:20

how is it possible that current flows in a circuit with capacitor since according to Ohm's law current is inversely proportional to resistance and insulator by definition has a big resistance, so we basically have an open circuit?

The short answer is because electrons can flow to and from a capacitor without the electrons having to pass through the insulation between the plates. The following qualitative explanation is offered:

Assuming the capacitor is not initially charged, then before it is connected to the battery each metal plate has an equal amount of protons (positive charge) and highly mobile electrons (negative charge) so that each plate is electrically neutral and there is no voltage (potential difference) between the plates.

When the capacitor is connected to a battery, the positive terminal of the battery attracts electrons off of the plate connected to it moving them to the positive terminal of the battery. This leaves a deficit of electrons on that plate making it positively charged.

Simultaneously, the negative terminal of the battery supplies an equal amount of electrons to the plate connected to it giving it a surplus of electrons making the plate negatively charged.

This moving of electrons from one plate to the positive terminal battery and from the negative terminal of the battery to the other plate is the capacitor current. Note that the electrons do not travel through the insulating material (dielectric) between the plates.

You can think of it roughly in terms of the electrons being "pulled" off one plate and "pushed" on to the other by the force of the electric field produced by the battery, but that the charges get "stuck" on the plates because they can't get past the insulating dielectric.

Eventually, as you already appear to know, the battery stops moving electrons between the plates when the potential difference across the plates equals that of the battery.

Hope this helps.

• Correct me if I am wrong, but how does the capacitor pass current when it is in series with an AC signal source? The current "passes" but not in the way that you expect. Since the voltage changes sinusoidally, the voltages also changes across the capacitor, which gives rise to an EMF that induces a current on the other side of the capacitor. This phenomenon is called the Maxwell displacement current: en.wikipedia.org/wiki/Displacement_current. I think you partially answered the question by providing half of the picture. – Tachyon Jun 11 at 22:04
• @Tachyon My answer applied to a battery, not an ac source. I contemplated bringing up displacement current but felt the OP was no where near that level. Wanted to keep it very basic. – Bob D Jun 11 at 22:11
• No worries, just trying to learn myself by explaining. If you want to master something, teach it, as Richard Feynman once said. – Tachyon Jun 11 at 22:15
• @Tachyon No truer words. Taught review classes for engineers taking the FE exam for many years. I liked to say, when you teach you learn, then you teach what you learned. – Bob D Jun 11 at 22:48
• @DarioMirić I think it is important to realize that, in contrast to a resistor, one can't have capacitor current unless the voltage across the capacitor is changing in time, as the relationship between current and voltage is $$i(t)=C\frac{dv(t)}{dt}$$ – Bob D Jun 12 at 13:28

The removal of electrons from the capacitor plate connected to the + terminal constitutes a current. As those electrons are removed for that plate, there is an accumulation of electrons on the other plate. That movement of electrons constitutes a current.

The current stops when the potentials of the capacitor plates are equal to the potentials of the respective battery terminals. This does not happen instantaneously, but rather has a time behavior because the transportation of electrons out of and into the capacitor requires time, and the potentials depend on the charge imbalance of the plates.

The presence of a parallel-plate capacitor means that in part of the circuit (only a small part; capacitors rarely have a gap as large as one millimeter) there is no movement of electrons, only a buildup of field (accompanied by electrons if the capacitor is not a vacuum type). This is problematic, because there is a simple way of detecting current, which is to observe the magnetic field that current creates, and PART of the circuit now no longer has current.

The fact is, that 'correction' to the magnetic field does not exist. The relevant Maxwell equation for current creating magnetism has a term added to the current displacement current, which is the rate of change of the electric field (like, the field inside the dielectric of a capacitor). That addition to the equation is not just necessary for circuits, it has the added side-effect that a changing electric field creates a magnetic field, even with NO charged particles in motion.

That term in the equation is why electromagnetic waves (light) travels in a vacuum. And, why charging of a capacitor is (in our measurements) indistinguishable from continuous flow of current in a circuit.

Literally, we can see the sun shine, because a capacitor gap in a circuit isn't distinguishable from continuous current through a circuit.

• Yes, thank you. I do understand the problem now. Displacement current just refers to the fact that electric field changes in time as capacitor is being charged which has an effect of creating a magnetic field according to Ampere's Law just like a real current does. I was kind of confused on this question since I know when circuits are opened, current doesn't flow. – Dario Mirić Jun 12 at 6:16
• When we have an open circuit, which is basically in simplest scenario two unconnected conductors placed in air (capacitor), capacitance of such a capacitor is so small that voltage of battery charges it so quickly that current very fastly stops flowing. – Dario Mirić Jun 12 at 6:16

A capacitor does indeed block direct current (DC). However appreciable alternating current (AC) can flow when the period of oscillation is less than the charging time of the capacitor.

• Well, if capacitor blocks direct current how can it be charged by a battery? Since charging a capacitor requires a current to flow through a conductor to accumulate charges on plates of capacitor. According to my understanding, as there is an insulator between the plates current shouldn't be able to flow and thus capacitor can't be charged. However, there is something I don't understand in this since capacitor can be charged by direct voltage sources like battery. – Dario Mirić Jun 11 at 18:19
• @DarioMirić, the same people who say "a capacitor blocks DC" do not consider a brief pulse of current to be DC. – Solomon Slow Jun 11 at 19:06
• Yes, strictly one should say that it blocks a steady state DC current. – Martin Vaughan Jun 11 at 19:08

A capacity (condenser) can be charged initially during the transitory build up of the charge on the capacitor when closing the circuit. Typically:

$$𝑡 = 𝑅.𝐶$$

With:

$$R$$: Resistance of the circuit.

$$C$$: Value of the capacity.

In fact, it also happens to be the mechanism behind the ability of the capacity to let through the time-variable component of a signal (current induced by the variation of a charge on the sides of a capacity), while blocking the constant component thereof.

Pumping electrons into one plate of a capacitor causes loose electrons on the other plate to be repelled when they "see" the other electrons coming in. This causes a brief pulse of electrons to flow out of one plate when electrons flow into and populate the other plate. For large plates, this brief pulse is long, and for small plates the brief pulse is short.

This means brief pulses of AC current can easily flow through a capacitor, while steady-state DC current is completely blocked.