# Does skin effect appear in home wires?

A technician said: Its better to use a solid cables for homes (not stranded cables).

I did not use any calculations but I think that stranded cables are better due to skin effect. We use 220V / 50Hz.

Is 50Hz too low frequency so that we can consider it as DC and "skin effect" has a very small effect at that frequency?

Is there any factors other than "skin effect" so that he recommends solid cables?

I'm speaking about cable that have 10 mm sq at most. And length is less than 20 m.

Thank you,

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Solid cable is cheaper and tends to stay where you put it. It also can't be frayed at terminals. – pjc50 Feb 24 at 14:05
Since the strands are in connection with each other, a stranded cable does not remove the problem with skin effect. If you're thinking of using litz wire, which consists of individually isolated strands and are designed to reduce the skin effect, then you must have a thick wallet! – pipe Feb 24 at 14:06
Unless you're using Litz wire, in which the individual strands are insulated from each other and woven in a special way to balance out the magnetic effects, there is no difference in electrical performance between stranded and solid wire of the same gauge. – Dave Tweed Feb 24 at 14:08
Solid core wire tends to have a smaller overall cross-section (thinner) than stranded does for the same area of conductor (copper). Just look at the markings on a wire stripping tool - the same size notch on the tool is used for a smaller gauge of stranded than solid. – brhans Feb 24 at 14:41

Skin depth is given by : $$\delta = \sqrt{\frac{1}{\sigma \pi \mu f}}$$ With in this case (approximate values) : $$\sigma = 6.10^7\text{ (copper's conductivity)}\\ \mu = \mu_0 = 4\pi 10^{-7}\\ f = 50 Hz.$$

Which gives $$\delta = 9.2 mm$$

So skin effect would be observed on cables with radius greater than 9.2 mm which means 18.4 mm diameter (3/4 inch) (or a 266 m² cross-section), which is very close to AWG(7\0), a gauge qualified to carry hundreds of amperes (while a domestic installation carries no more than 50 A). Since most cables for home are less than that, the skin effect is often and justifiably neglected in home electricity applications.

Also, the skin depth is the distance from the surface of the conductor to where the current density is damped to less than 1/e (36%) of its surface value. So in fact you would need even more diameter to observe the center of the cable having no current.

Regarding the choice between stranded and solid cables, solid cables are often preferred for home wiring for different reasons including cost, size, durability. Those have already been discussed in here : http://diy.stackexchange.com/questions/5901/why-are-homes-wired-using-solid-wire-rather-than-stranded

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Does that mean solid cables are better than stranded cables if the cable area is less than 9.2 mm? – Michael George Feb 24 at 14:02
What about the main cable of a home (the cable at the automatic circuit breaker) ? – Michael George Feb 24 at 14:06
Thank you very much :) – Michael George Feb 24 at 14:14
While it should mathematically be clear enough, I just sort of felt like pointing this out out loud, it's a Wednesday after all; 9.2mm radius, means 18.4mm diameter. That's close to 3/4inch for any USicans. Which is very close to AWG0000000 (AWG(7\0) for short), which is pretty much rated for 350A burried in insulation or 420+A only insulated in PVC. – Asmyldof Feb 24 at 14:55
It's also not clear what $\delta$ is. Current density decreases exponentially by $exp(-d/\delta)$ with the depth d. This means, in the center of a 9.2mm radius cable, the current density is still 37% of that at the surface. – sweber Feb 24 at 15:23

Skin effect really isn't an issue at 50 Hz and the cable sizes found in domestic properties. In any case normal stranded wire doesn't help you with skin affect.

In general a solid core wire is cheapest for a given size with finer stranding being more expensive. There are different sizes of strands used, for example in the UK i've come across solid core wires (twin and earth cable used for domestic wiring, very small single wires used in electronics), coarse stranded wires (common in conduit wiring and larger sizes twin and earth), normal flexible cables (i.e. what you would have in the mains flex of an appliance) and some super-flexible wires with extremely fine strands used for test leads.

Solid core wires (or for larger sizes wires with a few large strands) also work better with cheap/simple terminals. With fine stranded wire and many simple terminal types it's easy for only a small fraction of the strands to end up clamped in the terminal. Rising clamp terminals help avoid this but are more expensive.

The finer the stranding the more flexible the cable is. Flexibility can be both a blessing and a curse. If a cable is to be fixed in place then the more flexible it is the more support it will need to avoid sagging.

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