OHM’S LAW
PHYS0470 – Oct 2010, SDA & DGH
Experimental Goal
To explore macroscopic and microscopic aspects of Ohm’s law; to study the relationships
between resistivity, resistance, and carrier density in both two and three spatial
dimensions.
Apparatus and Materials
Several sheets of conducting paper, ruler, colored pencils, low voltage power supply,
multimeter, electrometer, cork board, mounting pins, coffee-hooks, clip leads, a plastic
tube w/ rubber-stopper electrodes, deionized-water, salt, and milligram scale.
Mount the paper to the corkboard with the mounting pins in order to make accurate
measurements of resistance and potential. To ensure good connection with the paper,
screw the hooks all the way into the cork board so the base of the hook touches the paint
on the paper. The colored (non-conducting) pencils are for drawing and recording the
results of measurements directly on the conducting paper.
The electrometers we use to measure potentials have very high input impedance - 200 T
(200x1012 ohms) - compared to the resistance of the paper (i.e., they draw an extremely
low current compared to the current through the paper). These meters are complex,
expensive, delicate instruments and should be treated with care.
Theory
Resistivity:
Definition of Resistance:
where is the resistivity, A is the cross-sectional area, and l, w, t are the dimensions of
the material
Fig. 1
When asked in the lab to measure the resistivity of the conductive paper, measure the
resistivity per unit thickness (ρ’), to avoid measuring the thickness of the paper.
Ohm’s Law:
Continuity Equation:
Top view
1 1
1
1 2
2
The dark lines are conductors
The current passing through circle 1 = The current passing through circle 2
By Ohm’s Law
Potential difference between 1 and 2:
2D Experiments
Equipotentials (between two points):
On the conductive paper with two points painted on it, attach the power supply to the
coffee hooks at each point and set the power supply to 25 volts. The points are located 5
cm from the horizontal center line (see Fig. 2). 1 cm from a coffee hook and on the line
connecting the hooks begin mapping an equipotential circumference – use a colored
pencil. Map a second equipotential circumference beginning 3 cm from the same hook.
You should have at least one closed equipotential (see Fig. 3). What would the
equipotential circumferences look like at 5, 7 & 9 cms from the same hook?
Hint: While holding one probe of the voltmeter where you wish to start your
equipotential, use the other probe to find points that have zero potential difference (use
the 20 volt scale).
Closed Equipotential
Point Charges
Fig. 2
Conducting Plane
Fig. 3
Fig. 4
Equipotentials (between a point and a plane):
Repeat the procedure above on the conductive paper one point and a line painted on it
(see Fig. 4). Connect the power supply to the point and the line and map same
equipotentials you did on the two point paper.
Using your knowledge of the geometric relationship between the electric field vector and
a surface of constant potential, draw in the electric field lines with another colored pencil.
Do this for both experiments (two points, and a point and a plane).
Upon completion of both experiments, go to the Electrostatics Simulation Applet, under
Useful Links on the lab wiki. Set up both scenarios on the simulation to check if you
correctly measured the equipotentials and electric field vectors. (Use Dipole Charge for
the first scenario, Charge + Plane for second)
Comment on the appearance of the equipotentials and electric field vectors in your lab
report. Compare the results of the two scenarios.
Ohm’s Law:
Measure the resistivity (per unit thickness) of one of the prepared and paper strips.
Report your result and include uncertainty. Describe the method you used. Compare
your value to the accepted value: Resistivity/Thickness = 20,000 ohms.
Measure the resistance between the two concentric circles on the two paper rings
provided. Compare their relative values to theory and their absolute value to your earlier
measurement of resistivity.
Apply a potential difference, V, between the inner and outer radii of the ring with the
smaller inner radius. Find the equipotential circumference corresponding to V/2.
Assuming that all equipotentials will exist on concentric circles, plot the potential vs
radius at 5 additional radii. Comment on the relationship amongst the radii and potential.
Are they consistent with theory?
3D Experiments
Conductivity of Water:
Refer to section 4.4 of Purcell before completing this portion; it gives a good introduction
to the physics of conduction and provides the background needed for this part of the lab.
A plastic insulating tube filled with water will be used as a resistor. Electrodes are
attached to stoppers on either end of the tube. First, polish the electrodes in the stoppers
with sandpaper, and then thoroughly clean the inside of the tube and the stopper
assemblies using tap water, mild soap, and paper towels. Rinse everything thoroughly
with tap water, and then rinse everything with deionized water. Fill the tube with
deionized water, dry the outside of the tube, and find the resistance of the water filled
tube by measuring the current through the solution for 4-5 different voltages. Do not use
the ohmmeter on the multimeter. Use this result to calculate the conductivity of “pure”
-1
water
.
Now dissolve a known amount of salt (about 0.1 grams) into the water. Use the scale to
accurately weigh the salt so you know how many Na and Cl atoms you add. One mole (
6 1023 atoms) of Na has a mass of 23 grams; one mole of Cl has a mass of 35 grams.
Check to see if your solution obeys Ohm’s law by measuring the current through the
solution at different voltages. Use these results to determine the conductivity of the
solution. Repeat these steps for at least two additional concentrations of salt. Plot your
data on a single graph on a computer in the lab. Remember to print out your graph.
Include the answers to the following questions in your lab report:
1. Why is the conductivity of pure water so low?
2. Why does adding salt increase the conductivity?
3. What is the electric field in the tube when 25 volts is applied?
4. What is the mean time between collisions of the ions? Assume Na and Cl ions have
the same mean time between collisions. (See Purcell, 2nd Edition, Sec. 4.1-4.4)
5. What is the average drift velocity of the ions in this field? Use the same
assumptions as in question 4. (See Purcell, 2nd Edition, Sec. 4.1-4.4)