


Resistance
Some materials conduct current better than others. If
we had a copper wire and a glass wire with the same length and cross
section, and put the same potential difference across them, the
current in the copper wire would be much larger than the current
in the glass wire. The structure of copper, a conductor, is such
that it permits electrons to move about more freely than glass,
an insulator. We say that the glass wire has a higher resistance, R,
than the copper wire.
We can express resistance in terms of the potential
difference, , and the current, I:
Generally, the is omitted. For a given
voltage, the larger the current, the smaller the resistance. The
unit of resistance is the ohm (). One ohm is equal to one volt per ampere: 1 = 1 V/A.
Ohm’s Law
Ohm’s Law relates the three important quantities of current,
voltage, and resistance:
This equation tells us that we can maximize the current
by having a large voltage drop and a small resistance. This is one
of the most important equations dealing with electromagnetism, and
SAT II Physics is bound to call upon you to remember it.
Example

Taking the initial voltage to be V and
the initial resistance to be R, the
initial current is = V/R.
The new voltage is 4V and the new
resistance is 2R, so the final current
is:
These changes double the current.
Resistivity
Resistivity, , is a property of a material that affects
its resistance. The higher the resistivity, the higher the resistance.
Resistance also depends on the dimensions of the wire—on its length, L,
and crosssectional area, A:
A longer wire provides more resistance because the charges
have farther to go. A larger crosssectional area reduces the resistance
because it is easier for the charges to move. The unit of resistivity
is the ohmmeter, · m. The resistivity
of copper is about 10^{–8} · m and the resistivity of glass is about 10^{12} · m. At higher temperatures, the resistivity
of most metals increases.
Example

As we know, the current in a wire is a measure of voltage
divided by resistance. We know that the voltage for the circuit
is 9 V, but we don’t know the resistance. However,
since we know that the resistivity for copper is 10^{–8} · m, we can use the formula for resistivity
to calculate the resistance in the wire.
First, we need to remember that area is measured in m^{2},
not mm^{2}. If 1 mm = m, then 4 mm^{2} = = m^{2}.
Now we can plug the values for the resistivity of copper
and the length and crosssectional area of the wire into the equation
for resistivity:
Once we know the resistance of the circuit, calculating
the current involves a simple application of Ohm’s Law:
Conductivity
Infrequently, you may come across talk of conductivity and
conductance rather than resistivity and resistance. As the names
suggest, these are just the inverse of their resistant counterparts.
Saying a material has high conductivity is another way of saying
that material has a low resistivity. Similarly, a circuit with high
conductance has low resistance. Someone with half a sense of humor
named the unit of conductance the mho (), where 1 = 1 .
