# How does length affect current carrying capacity

Will a wire have increased current capacity if the length is sufficiently small?

The reason I'm asking is that when doing PCB layout the vias often has thermal relief, which are small traces going from the via to track/fill around. But I've heard that because it's so short it doesn't really matter.

Is this true and can it be further extended to very short wires, or must you follow the rating of the wire?

If possible, how would one 'prove' that the wire can actually handle the current?

• What do you mean by "handle the current"? What bad thing will happen, in your case, if the trace can not handle the current? – Elliot Alderson Oct 23 '19 at 13:19
• those small regions do matter. Standard copper foil (1 ounce/foot^2) has thermal resistance of 70 degree Centigrade per watt PER SQUARE. With 4 of those regions, each with aspect ratio (estimated) of 1:2, thus each is 35 degrees/watt, you have 8.75 degrees/watt thermal resistance. Tho we should not pretend to precision here, but simply call it 10 degree C per watt. The key to this thinking is the 70 degree Centigrade per watt per SQUARE of foil. – analogsystemsrf Oct 23 '19 at 17:31

"Handle the current" basically involves two things:

• Does the wire remain at a reasonable temperature?

This requires calculating the power dissipation (I2R) per length of wire, and determining where that heat goes. You don't want the wire melting insulation or causing other temperature-related problems.

"Short" wires can sometimes take advantage of the fact the they're effectively connected to heat sinks at one or both ends (large terminal blocks, bus bars, etc.).

• Does the wire have excessive voltage drop?

The application will put constraints on how much voltage drop can be tolerated from one end of the wire to the other, which is a function of its total resistance and the magnitude of the current.

• dissipation ($I^2R$) per length of wire almost looks like the dissipation depends on the length of the wire... which of course isn't the case – Huisman Oct 23 '19 at 20:38
• @Huisman: Actually, for a given current, the total dissipation IS directly proportional to the length of the wire. But temperature rise is more closely related to the power per length, rather than the total length (or total power). – Dave Tweed Oct 23 '19 at 21:01