Resistance
Why does a copper wire have less resistance than an otherwise equivalent iron wire? And why is it that all
copper wires don’t have equal values of resistance? The resistance of an object is determined by three
characteristics of the object. The variable for resistance is R and the unit is ohms, symbol greek leter omega, .
1. Length. A short wire has a lower resistance than a long one*. Resistance is directly proportional to the length
of the path through which current flows: R  L. This means the longer the wire, the more resistance.
2. Cross-sectional Area. A thick wire (with a large cross-sectional area) has a lower resistance than a thin one*
(with a small cross-sectional area). Resistance is inversely proportional to cross-sectional area: R  1/A. This
means the larger the area, the less resistance.
3. Resistivity. A silver wire has a lower resistance than a lead wire*. Resistivity is a characteristic of a
substance (like density) and can be found in tables like the one below.
It is denoted by the lowercase Greek letter rho () and is measured in units of ohm-meters (Ω·m). Resistance is
directly proportional to resistivity: R  . This means the greater the resistivity, the greater the resistance. The
better a material is at conducting, the lower the resistivity, the lower the resistance.
Together, these proportionalities determine resistance by
the following relation.
This looks like something we have seen before, like yesterday. If capacitors are the mature older sibling that is
responsible and saves energy, then resistors are the irresponsible younger sibling that using energy wild and
free. In other words, capacitors store energy to provide it to a circuit and resistors spend energy and remove it
from a circuit. Compare the two equations:
and
So, large area and small distance makes for LARGE capacitance. Small area and big distance makes for
LARGE resistance, they are opposites of each other.
So, a good resistor would be a long, narrow wire that is a bad conductor. However, this would make the
circuitry inside of electronics very large. To make things smaller, this wire can be wrapped into a coil. To see
how these types of objects have high resistance and steal energy, go run your toaster without bread in it. Those
coils have high resistance and take energy from the circuit and release it as heat to toast the bread. Some
resistors release energy as light, think the filament in a bulb. In either case, electrical energy is being converted
by a resistor into another form of energy.
The resistors we will use will be made of ceramics. When we build circuits in this class, please remember,
resistors get HOT! If you touch them immediately after running electricity through them, they will be HOT!
Resistors can be made of a variety of different materials. Look up and read the pages in your book about
resistance, resistivity, semiconductors and superconductors.
When asked conceptual questions about resistors, you might see images like this:
Pretend they want to know which wire would have the most resistance…
Well, if you are looking at loops of wire, the outside one is going to have the most
resistance because it is longer. However, if this diagram is showing the relationship
between the cross-sectional areas of the wires, then the outside wire has a larger
area and would have less resistance. Be careful to understand what they are
showing you with the figure.
Questions to answer about resistors.
1. What quality of metals make them good resistors?
2. What are semiconductors? Superconductors?
3. Nichrome wire, with a diameter of 0.81 mm is wound into loops to form a resistor coil. If each loop has a
diameter of 0.5 cm and there are 200 turns (fancy word for loop), what is the resistance in the coil?
4. A coil of copper wire with a diameter of 0.12 mm has a resistance of 2 . Calculate the length of the
5. The four wires at the right are made of the same material. Which has the
greatest resistance? Which has the least resistance?
The Book of Phyz
Dean Baird
1/21/08