25.5 - Resistivity
Resistivity is used to quantify how much a material resists the flow of current. It is
represented by the Greek letter ȡ (rho). A material considered a good conductor, such
as copper, has low resistivity. Materials used as insulators, such as glass or rubber,
have high resistivity.
Resistivity is the inverse of conductivity (which quantifies how well a material conducts
current). Current does not readily flow through materials with very high resistivity. As the
table in Concept 2 shows, there is an enormous range in the resistivity of materials.
The table includes nichrome, an alloy of nickel and chromium. Due to its high resistivity,
Nichrome is commonly used in hot plates, toasters and other electrical appliances that
generate intense heat. Its large amount of resistivity causes electrons in the current to
lose energy to the nichrome atoms, increasing their thermal energy.
Extension cords, designed to allow current to flow safely from one point to another, take
advantage of the relative resistivities of materials. The cords typically are composed of
copper wire, a material with low resistivity, surrounded by rubber or vinyl, materials with
high resistivity. Electrical current flows readily through the copper, but not through the
material that surrounds it.
Resistivity is a property of a material. Its units are the ohm·meter (·m). In contrast,
resistance is the property of a component like a resistor or the filament in a light bulb.
Resistivity is one factor that determines a resistor’s resistance; the other factor is the
geometry of the resistor. The longer a resistor, the greater its resistance; the wider it is
(the greater its cross sectional area), the less its resistance. Again, water can be used
to provide an analogy: a long, thin pipe resists the flow of water more than a short, fat
one.
The equation used to calculate resistance as a function of a resistor’s geometry and
composition is shown in Equation 1.
The problem in Example 1 asks you to compute the amount of resistance found in a
segment of copper wire. The resistance of resistors that are sold in electronics shops
runs from the tens of ohms to the thousands of ohms and beyond. When electric circuits
are analyzed, the resistance of wire is often ignored because it is relatively insignificant.
The low resistivity of wire, along with Ohm’s law, helps to answer a question physicists
like to pose: Why can a bird safely stand on an unshielded high voltage line? Why does
the bird not get injured as current flows up one of its feet, through its body, and down
the other foot?
The answer is that the potential difference is very small across the segment of wire
involved because the wire’s resistance is quite low. Its resistance is low because the
segment is wide and short and is made of a material with low resistivity. Ohm’s law
states that the potential difference is the product of the current and the resistance. With
low resistance, there is very little potential difference. With very little potential difference,
effectively no current flows through the bird.
Do NOT test this out yourself. High voltage lines are enormously dangerous. If you
touch such a line while standing on the ground, you are providing a path for current to
flow from the wire to the Earth. The potential difference between these points is
enormous, and the resulting current could kill you.
Resistivity
Inverse of conductivity
·Conductors have low resistivity
·Insulators have high resistivityTable of resistivities, ȡ
Resistance
Depends on resistivity, configuration of
material