Busbar AC Resistance Calculator
A busbar is not a round wire, so the Kelvin-function solution does not apply. This gives two models: the exact one-dimensional strip result, which is right when the bar is much wider than it is thick, and a perimeter-shell approximation for stockier sections. The page picks whichever suits the aspect ratio and shows both.
Choosing something to solve for makes AC resistance an editable target and computes the chosen input from it.
Formula
| w, t | bar width and thickness (m) |
| n | bars in parallel per phase |
| delta | skin depth at the operating frequency (m) |
| x | thickness in skin depths |
| A | cross-section of one bar (m^2) |
What this model assumes, and where it stops
Assumptions
- A single isolated bar per phase, or parallel bars far enough apart not to couple.
- Uniform rectangular section along the whole run.
- Sinusoidal current at one frequency; the current given is RMS.
- Non-magnetic conductor, so relative permeability is 1.
- Isothermal bar at the temperature entered.
Limitations
- Proximity effect is not included, and on a real three-phase busbar system it is usually larger than the skin effect this page computes. Adjacent phases push current to the far faces of each bar.
- Parallel bars on the same phase share current very unevenly once spacing is comparable to bar width - the outer bars carry substantially more.
- The two models disagree for square-ish sections, and neither is right there. Treat a large gap between the strip and shell numbers as a warning that you need a field solution.
- The shell approximation ignores the corner current concentration that a real rectangular bar shows.
- Steel enclosures, mounting hardware and nearby ferrous structure all add eddy losses that no closed form here represents.
- No account of joints, bends, or the transition to terminations.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Three-phase busbar systems, where the proximity effect between phases dominates and depends entirely on the spacing and arrangement.
- Parallel bars per phase, where current sharing is decided by geometry, not by equal division.
- Laminated and sandwich busbar assemblies.
- Bars inside steel enclosures, where induced enclosure currents add loss and heat the assembly.
- Corner and edge current concentration, which sets the local hot spot on a heavily loaded bar.
- Bends, tees and terminations, where the uniform-section assumption fails entirely.
Common questions
Does 50 Hz skin effect matter in a busbar?
Barely, for a single bar of ordinary thickness. Skin depth in copper at 50 Hz and 20 degC is 9.2 mm, so a 10 mm thick bar is about one skin depth through and a 100 x 10 mm bar shows Rac/Rdc of only 1.008. It starts to matter for very wide or very thick sections, at 400 Hz, or when several bars are paralleled - stacked laminations shield each other and the ratio climbs well above what this isolated-bar model shows.
Why does a flat bar have less AC resistance rise than a round conductor of the same area?
A thin wide strip puts nearly all its metal within a skin depth of a surface, so the current has somewhere useful to crowd. A round conductor of equal area concentrates metal in the middle where high-frequency current refuses to flow. This is exactly why busbars are flat, and why the model brackets the answer between a 1D strip solution and a perimeter-shell limit.
Does this include proximity effect between phases?
No - this page models one isolated bar. Adjacent phase bars distort each other’s current distribution and raise the effective resistance further, worst for closely spaced flat bars face to face. If the phase spacing is less than about twice the bar width, treat this result as optimistic and check with a field solution.
References
- Copper Development Association - Publication 22, Copper for Busbars
- Ramo, Whinnery & Van Duzer - Fields and Waves in Communication Electronics, 1D conductor solution