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For a certain application, I'm using carbon based brushes to transmit power from a stationary component to a moving component. I'd like to calculate the resistance of the carbon based brushes to know the maximum current it can carry without problems. I did the same with the copper using the following formula:

$$R = \frac{\rho L}{A}$$

Is it valid to use the same formula with the brushes?

Where the resistivity of carbon is: 2.50E−6 to 5.00E−6

Also, if low voltage and high current is applied between the surfaces of each component is an arc possible? There should be no gaps at all, all surfaces are in direct contact.

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    \$\begingroup\$ Arcing is only going to occur if there's lots of power and a gap develops (think arc welding...), but unless you're moving several tens of amps or a hundred volts or so, any arcs that develop probably won't last long - they just won't have the power to keep going. \$\endgroup\$ – Sam May 24 '16 at 11:22
  • \$\begingroup\$ Does say (without specifying) "high" current. \$\endgroup\$ – Ecnerwal May 24 '16 at 14:12
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schematic

simulate this circuit – Schematic created using CircuitLab

I think you'll find the resistance dominated by the rotating interface between the carbon and the copper, not by the carbon.

My general experience suggests that arcs a quite possible, but I guess that is mostly with slotted motor armatures rather than dead-smooth slip rings. But I'd hesitate to assume otherwise without testing.

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