# Resistance of capacitors

Please I would like to know how the resistance of the plates of a capacitors work? Is it the same as a resistor? If yes, is there electric field inside the plates like inside a resistor?

Actually, the capacitor is an open circuit. It has infinite resistance. (I will assume a DC circuit.)

But since the plates are so close, charge build up on one plate induces charge in the opposite plate of the opposite sign. This means that putting a battery across a capacitor (see the picture below) will let negative charge (in the form of electrons) flow to one plate, and this negative net charge will repel and push negative charge away from the opposite plate (leaving behind a net positive charge).

In the moment that you turn on the current in the circuit (as "closing" the switch in the picture), current runs as if there was no blocking (corresponding to 0 resistance). Charge flows to the plate and pushes the same amount of charge away from the other plate. From the outside this looks as if it was just a wire.

After a while no more charge is build up on the plates. Then no more charge is being pushed around. Now the gab actually acts like a hole in the circuit - as a clipped wire - as if it had infinit resistance.

Between start and some long time $t$ later, charge will gradually build up towards it's max-value and therefor current will gradually decrese towards zero (corresponding to resistance gradually increasing towards infinity), as this graph shows:

The dotted line is the current - it starts high, and ends low. The red line is the charge build up. The voltage over the capacitor is constant, so if you want to find the equivalent "resistance" $R_{eq}$ (which will change with time), use Ohm's law:

$$U=R_{eq}(t) \cdot i(t)$$

Just remember that it is not resistance in a physical material as in the usual way.

• I am talking about capacitor's plates which are a conductive materials thus about ESR and not about the dielectric resistance between the plates. – Tonylb1 Feb 16 '15 at 14:08
• This is an off topic comment, but can I know how do you draw those circuits in here? I mean is there any software for doing this? – Aneek Sep 5 '16 at 13:57

I agree with both of the two answers above. But I would also suggest that the term resistance should not really be applied at all to a capacitor ( I think it leads the question astray ) Going to the more general notion of impedance ( I would use the complex formulation ) the question makes more sense to me. This immediately brings in the importance of frequency. For real, as opposed to ideal, caps the concept of equivalent series resistance, ESR, is in a sense the resistance of the cap, but I may be straying.

• You might want to consider expanding on the notion of impedance vs resistance here. It might elucidate future readers as to why it is better to think this way. – Kyle Kanos Feb 16 '15 at 14:08

A capacitor has an infinite resistance (well, unless the voltage gets so high it breaks down). The simplest capacitor is made from two parallel plates with nothing but space in between - as you can guess from its electronic symbol.

In a DC circuit, a capacitor acts as an open circuit and does not permit current to pass. In an AC circuit a capacitor has an effect because it acts as a current reservoir while the current is changing. This can have the effect of smoothing the current spikes so it performs a damping effect.

• I am talking about capacitor's plates which are a conductive materials thus about ESR and not about the dielectric resistance between the plates. – Tonylb1 Feb 16 '15 at 14:49

So the thing you will want to look up is parasitic resistance in a capacitor and an inductor has the same thing. In the real world these types of devices must have a resistance becuase we do not have ideal resistors, capacitors, inductors, and the like. On the other hand when looking at a circuit problems in school you will work with ideal sources in which the other answears cover fairly well.