# Why don't charges build up on wires like plates of a capacitor?

Suppose you have a parallel plate capacitor and you want to charge it by using a battery. You will connect the plates with the two terminals of the battery. Now my book says that the charges will get accumulated on the plates of the capacitor. The amount of charge will be equal to the capacitance times the voltage of the battery. But what about the wires they are also on the same potential why don't charges accumulate on the wires? I have come across this many a times in capacitor circuits where wires don't get any charge, all the charges accumulate on the capacitors but I just don't understand why.

• Wires do have capacitance and charges accumulate. The total capacitance depends on the wire diameter and how far it is from other conductors, a good rule of thumb is to estimate the capacitance of a wire as 10-20 pF/m. When the wire is part of a twisted pair or coaxial cable, one has to assume closer to approx. 100pF/m. If we connect these wires to really large capacitors, the wire capacitance doesn't matter (it's more likely that the wire inductance or resistance will), but in precision AC circuits and even more so in RF circuits understanding these wire impedances is absolutely crucial. – CuriousOne Jul 16 '16 at 8:24
• Have a look at Surface charges on circuit wires and resistors play three roles J. D. Jackson Am. J. Phys. ${\bf 64}$, 855 (1996). – jim Jul 16 '16 at 12:24
• A wire provides a path of relatively lower resistance. So electrons umder the influence of an external emf flow(very less accumulation) . On the other hand, capavitor plates srparated by a dielectric is a path of high resistance, which very few electrons can overcome (some can, is the distance is small, but most accumulate due to lavk of sufficient energy) – Lelouch Jul 16 '16 at 13:59

## 1 Answer

Because it seems to constitute a complete answer, I am reproducing the comments of Curious (after some editing) as a Community Answer :

Wires do have capacitance and charges accumulate. The total capacitance depends on the wire diameter and how far it is from other conductors. A good rule of thumb is to estimate the capacitance of a wire as $10-20 pF/m$. When the wire is part of a twisted pair or coaxial cable, one has to assume closer to approx. $100pF/m$.

If we connect these wires to typical capacitors - around $0.1\mu F$ upwards - the wire capacitance is insignificant. It is more likely that the wire inductance or resistance will have a greater effect. But in precision AC circuits, and even more so in RF circuits, understanding these wire impedances is absolutely crucial.

Jim suggests :

Have a look at Surface charges on circuit wires and resistors play three roles J. D. Jackson Am. J. Phys. 6464, 855 (1996).

This article is available free (but by request) at ResearchGate (https://www.researchgate.net/publication/243491901). The Abstract states :

In general, the conductors of a current-carrying circuit must have nonuniform surface charge densities on them (1) to maintain the potential around the circuit, (2) to provide the electric field in the space outside the conductors, and (3) to assure the confined flow of current.... We illustrate these ideas with a circuit consisting of a resistor and a battery connected by wires and other conductors, in a geometry that permits solution with a Fourier-Bessel series...