Resistance

Resistance is a measure of the degree to which an object opposes the movement of electric charge. The word object is load-bearing: this wire, of this length, this thickness, this material. The sheet supplies the geometry,

with $\ell$ the length along the direction the charge travels and $A$ the cross-sectional area perpendicular to it. Double the length and $R$ doubles. Double the diameter and $R$ drops to a quarter, because area goes as the square of the radius. Stretch a wire to twice its length at constant volume and $R$ quadruples, since the area halves as the length doubles.

The unit falls out of Ohm's law rather than needing to be memorized: $1\ \Omega = 1\ \text{V/A}$.

Ohmic and not. A material that obeys Ohm's law has constant resistance for all currents. Plot current against potential difference for such an element and you get a straight line through the origin whose slope is $1/R$. A filament lamp bends that line, because heating the filament raises its resistivity.

What this entry deliberately leaves alone is the algebra. Rearranging $I = \Delta V/R$, deciding which form to use, and pushing it through series and parallel networks belong to the Ohm's law guide and the Ohm's law calculator.