# Does a capacitor have a resistance?

Does a capacitor have a resistance? And why? When I asked my physics teacher, he said certainly not, but I didn't figure out why. Can anyone please clarify? Thanks in advance.

• Physical capacitors are often modeled as an ideal capacitor with a small series inductance and resistance along with a small parallel conductance. However, an ideal capacitor, by definition has only capacitance, i.e., $i_C = C \frac{dv_C}{dt}$ would not hold otherwise. – Alfred Centauri May 20 '17 at 12:55

## 3 Answers

If you are dealing with a real capacitor, it has for sure parasite resistances, you may model it as follow

Where $Rs$ is the equivalent serie resistance, $Rp$ the parallel one, and the capacitor in the circuit, is intended to be an ideal capacitor which of course has not parassite resistances.

The question you have put forward is fairly straight forward and honest. Firstly, Resistance to charge flow in a conductor originates primarily due to inelastic collisions of the electrons with the atoms in the material medium. You can understand this by looking at the momentum equation from Drude theory.

$$dp/dt=qE+ \delta({p}_{collision})/{\tau}$$ where $\tau$ relates to the average time between two collisions.

Since the capacitor is basically a charge storage, there is no such equation as this hence you can say there is no electrical resistance.

But if you define resistance by its truest meaning, the capacitor is resistant to low frequencies but allows high frequency currents to pass through. The impedance (or equivalent resistance) for a capacitor is $1/\omega C$ where $\omega$ is the current frequency and $C$ the capacitance. For DC, $\omega=0$ and hence the impedance is infinite. But for non-zero frequencies, it is finite and hence high frequency currents can pass through.

• "But if you define resistance by its truest meaning, the capacitor is resistant to low frequencies" - in the phasor domain (sinusoidal excitation), resistance is the real part of impedance but the impedance of an ideal capacitor is purely imaginary, i.e., has zero real part. In this sense, a capacitor has zero resistance at all frequencies. – Alfred Centauri May 20 '17 at 20:07
• Yes true. That is a clearer answer. Then the DC blocking ability of a capacitor which arises of out polarization in the dielectric should not be termed as resistance anyhow. – ARC May 21 '17 at 4:51

I feel, capacitor has infinite resistance, since charge generally does not flow through a capacitor, it stores the charge. It generally has a dielectric medium which does not conduct electricity. Thus its resistance will be same as the resistance of the medium. Very high voltage has to be applied across it so that current flows.

• A capacitor in practical never has air between the plates, but some other dielectric medium. But it's resistance is ideally infinite. – Wrichik Basu May 20 '17 at 13:25
• It is true only for stationary currents. That is why you replace the capacitors​ with open circuits, in the stationary current analysis. – Dante May 20 '17 at 13:31
• @Dante Yes, sure, I meant that. – Wrichik Basu May 20 '17 at 15:55
• @WrichikBasu "A capacitor in practical never has air between the plates." That is not correct. See orenelliottproducts.com/index-1.html, or rfparts.com/capacitors/capacitors-airdie.html. One application is in high voltage applications, e.g. up to 10 kV across the cap. – alephzero May 20 '17 at 20:56
• @alephzero I didn't know about that. Yes, air may act as a dielectric. – Wrichik Basu May 20 '17 at 20:57