Download Resistors and Resistivity©98

Resistors and Resistivity©98
Experiment 9
Objective: To learn to build simple electrical circuits, to read electrical meters and to
verify Ohm’s Law and calculate resistivity.
DISCUSSION:
Electrical circuits behave like an enclosed plumbing system, such as the
circulatory system of the body. There is an “electron pump” which is analogous to the
heart in its function. This pump may be a dry cell, battery or generator. There is a fluid
of electronic charges (either electrons or holes – the absence of an electron), analogous to
the blood. There are wires or conductors, analogous to the veins or arteries.
It is important to remember that the wires always have electrons in them and that
the battery or generator is not a source of electrons. Rather the battery or generator
simply pushes the electronic charges (electrons or holes) already in the wires around the
circuit.
Electrical meters are devices that measure certain characteristics of this flow of
electrons. The ammeter is an instrument that measures the current – flow of electric
charges. The unit of this measure if the ampere (SI symbol, A), which represents the
flow of one coulomb per second by a give point in the circuit. The ammeter has a very
low resistance to the current in order that, when it is placed in the circuit, it does not
impede the current.
The voltmeter is an instrument that, loosely speaking measures the drop in
electrical ‘pressure’ between any two points in a circuit. More exactly, it measures the
energy per unit charge that is dissipated or generated between these two points in a
circuit. The unit of this measure is the volt, which is equivalent to a loss or gain in
electrical potential energy of one joule per coulomb. The voltmeter has a very high
resistance to the flow of electricity in order that, when it straddles two points in a circuit,
a new path for the current is not created.
Voltages are generated by such things as batteries and electrical generators.
Voltages are lost or dissipated by such things as wires, motors, electrical lights, and all
other devices used to convert electrical energy into energy of some other form.
Ohm’s law states that the voltage V dissipated or lost between two points in a
conducting medium is proportional to the current I between those two points. That is,
V I
or
V  IR
(1)
9-1
where R is a constant of proportionality. This constant is known as the resistance of the
medium between the points in question. Ohm’s law states, in other words, that the
resistance between the points is constant. (Actually, Ohm’s law is not exactly true in the
case of many materials, and in some cases it fails completely. These are disingenuously
described as non-ohmic materials.)
Every material has a resistivity, ρ, associated with its chemical composition, its
size and shape and its temperature. It is related to the material’s resistance by its length
and cross section area:
AR

(2)

where A is the area, R is the resistance and ℓ is the length. For a cylindrical shape, this
becomes
r 2 R

(3)

where r is the radius of the cylinder. It is this property of resistivity that determines if a
material would make a good resistor. If the material’s resistivity is very high, the material
can be used as an insulator.
EXERCISES:
Resistance and length:
A
1. Choose a color of PlayDoh. Record this color.
2. Divide the Play-Doh in
half. Divide one of these -18 +18
halves in half again.
3. Flatten the two small
pieces of Play-Doh into
thick pancakes, covering
the ends of the copper
Figure 1: Wiring the Play-Doh pancakes.
pieces.
4. Connect the positive lead of the power supply to the positive jack on the ammeter.
See Figure 1.
5. Connect the negative jack of the ammeter to one of the copper pieces under a
pancake.
6. Connect the negative lead of the power supply to the other piece of copper under
the other pancake.
7. Using the other half of the Play-Doh, roll a 30 cm long cylinder. Try to make it as
uniform in shape as possible.
8. Measure and record the length and radius of this cylinder.
9-2
9. Complete the circuit by placing the ends of the cylinder on the pancakes. You
might have to slightly flatten the end of the cylinder to make good contact. See
Figure 2.
10. Connect the positive lead
A
of the voltmeter to a
copper piece and lay it
V
sideways on the positive
end of the cylinder.
-18 +18
11. Connect the negative
lead of the voltmeter to
the other copper piece
and lay it sideways on
the negative end of the
Figure 2: Measuring the voltage and current of the complete circuit.
cylinder.
12. Wait until the readings stabilize and then record the voltage and current.
13. Unhook the voltmeter and remove the cylinder.
14. Cut 5 cm off the cylinder and record the new length.
15. Reconnect the circuit and record the new voltage and current.
16. Repeat steps 14 and 15 until your left with a 5 cm piece of cylinder.
Resistance and color:
Repeat the previous experiment with two additional colors of Play-Doh.
Analysis:
1. Using Eq. 1, calculate the resistance for each voltage and current pair of
readings.
2. Calculate the area of each cylinder.

3. Calculate the value of
for each length.
A

4. For each color, graph Resistance vs. .
A
5. Find the slope of each of these graphs. This value is the resistivity of that
color of Play-Doh.
Questions:
1. As the length of the cylinder shortened, what happen to the resistance? Why
do you think this happened?
2. Are the resistivities of the different colors the same? Why do you think they
are the same/different?
3. What so you think would happened to the resistance if we had changed the
radius instead of the length of the cylinders?
9-3
Resistors – Data Sheet
Play-Doh Color:
Cylinder Radius:
Cylinder Area:
Length Voltage (V)
0.30 m
0.25 m
0.20 m
0.15 m
0.10 m
0.05 m
Play-Doh Color:
Cylinder Radius:
Cylinder Area:
Length Voltage (V)
0.30 m
0.25 m
0.20 m
0.15 m
0.10 m
0.05 m
Play-Doh Color:
Cylinder Radius:
Cylinder Area:
Length Voltage (V)
0.30 m
0.25 m
0.20 m
0.15 m
0.10 m
0.05 m
(m)
(m2)
Current (A)
Resistance (Ω)
Length/Area
Resistance (Ω)
Length/Area
Resistance (Ω)
Length/Area
(m)
(m2)
Current (A)
(m)
(m2)
Current (A)
9-4
Resistors – Data Sheet (con’t)
9-5
Resistors – Data Sheet (con’t)
9-6
Resistors – Data Sheet (con’t)
9-7
9-8