ampacity, wires vs metal plates

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I've been trying to wrap my head around this. Normally the current capacity is the surface area of the conductor, but plates are always preferred when i see videos of people making batteries to connect cells and components instead of cables. Aside from the mechanical expect, the current capacity of a wire is determined by its diameter (or circular area), but what about metal plates? is it determined by the area as in the whole surface area of the plate or between the connections? So if you had a metal plate with 1mm of thickness, and 20cmx10cm (lengthxwidth), is the current capacity determined by 1mm of thickness and 10cm of width from one end to the other or is it a lot more?

[TimFox]

At DC, the resistance of a conductor is determined by its cross-section area (perpendicular to the direction of current flow).
Therefore, the relevant parameter is either the area of the rectangular cross section or the circular cross section.
At AC, you must take skin effect into account.  At 50/60 Hz, you rarely see larger than 0.75 inch = 19 mm for thickness for that reason, but at RF the skin depth is measured in micrometers and the surface area is the relevant parameter when comparing different geometries at the same frequency.
Ampacity complicates things, since it includes the dissipation of heat away from the conductor to keep below an acceptable temperature rise.

[TheMG]

When talking about DC, it's the cross-sectional area (in case of a flat conductor, that would be the thickness multiplied by the width) that determines the current handling capability.

Other factors to consider are the conductor material, allowable voltage drop at rated current, and allowable temperature rise of conductor.

[Haenk]

IMHO plates have two advantages:
space needed
clean setup
impuls welding to contacts
That's three advantages.
Current etc. is probably not the largest issue, as long as the plate has enough area (broad x thick), the weak point is the welded contact.

[Gyro]

The other factors that may come into play are...

1. How the conductor is terminated and the danger of localised heating - Obviously a flat strip is far more suited to a bolted connection or welded connection to a battery tab, whereas a circular conductor is more suited to round terminal clamps.

2. Higher surface area to cross sectional area ratio improves thermal dissipation.

Both of these factors become important as the current goes up.

[T3sl4co1l]

It's both.  Cross section begets power, but surface area begets temperature rise.  So, based on pure physics, assuming we want a given limiting temp rise -- it depends.  It's not a straight proportion to either quantity, nor is it a straightforward 3/2 or whatever power law.  (Well, it's probably close to a 3/2 power law, but it'll be some odd exponent near there, that comes from the convection rate as well as these factors.)

We normally assume fixed current density, i.e., cross section proportional to rating.  But this does overestimate capacity at high currents, and under- at low.

A full model isn't easy, because it depends on the convection rate (or conduction for that matter, when potted).  Which is nonlinear, and depends on enclosure (conduit? equipment? free air?) and orientation.

Plates have the advantage that cross section is just, whatever size you cut it to, it's very flexible that way; and, they have lots of surface area.  They can also be arranged broad-facing to lower inductance, in circuits where that matters (industrial converters, pulse generators).

Or board-level SMPS for that matter, since PCBs are arguably just made with very thin plate, and benefit from the low inductance and modest dissipation, hah.

The surest answer is: check the NEC or whatever local code, and follow that.  I mean -- this isn't even a matter of physics, it's simply the law!

Or if it's for equipment rather than facility wiring, this is still a fine starting point.  You can shave it down from there, as long as it's not a fire hazard (passes UL/etc.), and it meets functional requirements (temp rise within some reasonably acceptable range, voltage drop / power dissipation acceptable).

Equipment still isn't a free-for-all, like, UL will test conductors connected to mains wiring, for certain overload conditions (with the fuse bypassed as part of the test!).  Usually you'll have to skimp quite severely to run afoul of this.  Standard wire sizes, connectors of approved ratings, should be fine.  Like, maybe the most likely case is PCB traces burning off, because, well, they're just thin foil, and sometimes you can't afford much more width than is needed for nominal current rating only.

Tim