Cracking the SAT Physics Subject Test

RESISTANCE

Let’s say we had a copper wire and a glass fiber that had the same length and
cross-sectional area, and that we hooked up the ends of the metal wire to a source
of potential difference and measured the resulting current. If we were to do the
same thing with the glass fiber, the current would probably be too small to measure,
but why? Well, the glass provided more resistance to the flow of charge. If the
potential difference is ∆V and the current is I, then the resistance is

Notice that if the current is large, the resistance is low, and if the current is small,
then resistance is high. The ∆ in the equation above is often omitted, but you should
always assume that in this context, V = ∆V = difference in electric potential, also
called voltage.

Resistivity

The resistance of an object depends on two things: the material it’s made

of and its shape. For example, again think of the copper wire and glass

fiber of the same length and area. They have the same shape, but their

resistances are different because they’re made of different materials.

Glass has a much greater intrinsic resistance than copper does; it has a

greater resistivity. For a wire of length L and cross-sectional area A

made of a material with resistivity ρ, resistance is given by

The resistivity of copper is around 10−8 Ω • m, while the resistivity of

glass is much greater, around 10^12 Ω • m.

Because resistance is voltage divided by current, it is expressed in volts per amp.
One volt per amp is one ohm (Ω, omega). So, 1 V/A = 1 Ω.