# Skin effect - resistance changes during DC/AC variation

I have a question about skin effect, skin depth to be exact.

Consider an AC system and a wire in it. Skin depth is, let it be, 0.2 radius of it. We know that if it was a DC system, it would spread the current evenly and then the resistance would be lower than in AC system (according to - bigger surface "makes" lower resistance).

My question is - is it possible to tell exactly how many times did the resistance decrease (comparing DC with AC)?

• There are plenty of examples if you google. – Andy aka Nov 8 '16 at 19:39
• So is it just a ratio between two surfaces (piR^2 vs piR^2 - 0.8pi*R^2)? There won't be any other information, just value of skin depth and both AC and DC system. – adek111 Nov 8 '16 at 19:44
• There are ac resistance calculators on line and more often than not these will give formulas. – Andy aka Nov 8 '16 at 20:22
• In reality, the wire will also show inductive behaviour, which will also increase the impedance with frequency. Noticeable skin effect normally occurs at much higher frequencies. – DPF Nov 8 '16 at 21:09

In short - no, it can’t be done exactly :)

### Why not?

The resistance accounts for all active power losses in the wire. The losses are a sum of different effects, some of which are modeled by theories (such as skin effect, magnetic hysteresis losses, eddy currents in conductors near the wire, the corona-effect, etc). Other loss factors are usually not very well modelled in electrical engineering applications, and are usually just bunched together and just called excess losses. The excess losses are then estimated by some measurement at a specific operating point. Examples of excess losses: could be some capacitive (electrostatic) coupling with nearby conductors leading to moving currents, electromagnetic waves being emitted due to an antenna-like geometry, weird stuff with the magnetic domains on a molecular level, and so on.

### Approximatively then

Wikipedia has a nice article about the skin effect, and with some approximation formula for how much the resistance will increase due to the the skin effect only (but maybe that was what you were asking for?) in round conductors.

https://en.wikipedia.org/wiki/Skin_effect

### Next level

I can recommend Power System Analysis by Grainger, which can probably be borrowed at some technical library close to you, or maybe online? A lot of worked examples on different transmission line setups with different inductances etc. If you want the full truth about how skin depth is derived I would recommend Electromagnetic Fields by Wangsness. Prerequisite for both books is 1st year calculus at university level. (if any moderator thinks I sound like an ad, please edit this paragraph away)