Ohm's Law -- from Eric Weisstein's World of Physics

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Ohm's Law

The current I is related to the surface integral of the current density J by

where use has been made of the relation

with the conductivity and E the electric field. If is constant, then

Now, for a wire, E and are constant and perpendicular, so

where A is the cross sectional area, V is the voltage, and L is the length of the wire. Plugging in gives

Defining the resistance

and solving for V gives Ohm's law,

Current, Ohm's Phase Law, Resistance, Voltage