The Electrical Resistivity of Graphite
In this activity you will calculate the electrical resistivity of graphite. You will need a graphite pencil, paper, and a Volt Ohm Meter (VOM).
1. Using a graphite pencil, draw a line about 5-cm long and 3 -mm wide on a sheet of paper. Keep the width as uniform as possible. Repeatedly draw on the line until it appears completely dark.
2. Now set the multimeter to measure ohms. Use the two VOM probes to measure the electrical resistance of the line. Touch the blunt edge of a probe to each end of the line.
The greater the value of , the greater the resistance of the line. The following formula will be useful in understanding the relationship between electrical resistivity and the variables that determine it. The measured resistance (R) of a material is equal to the electrical resistivity of the material times the length (L) over which the resistance is measured, divided by the cross-sectional area of the material (A). In other words:
R= L/A
Suppose that you measured the resistance of the line to be 3x104 ohms, so
R= 3x104 ohms. The distance between the probes on the line is 5 cm, so L = 5 cm. If the line is 3-mm wide, then W = 0.3 cm. The thickness of the line must be estimated and is on the order of 10 micrometers or 10-3 cm, so T=10-3 cm. Therefore, the cross-sectional area:
Area =Width x Thickness =(0.3 cm)(10-3 cm) = 3x10-4 cm2.
Now can be calculated.
RA/L = (3 x 104 ohm)(3x104cm2)/(5 cm)
The electrical resistivity of graphite can range from about 104 ohm-cm to 10 ohm-cm. Values of 0.1-10 ohm-cm are typically measured in these experiments.
B. The relationship between resistance and length.
1. Lightly draw a line 3-mm wide and 5-cm long. Draw a second line with the same dimensions as the first, but make it heavy and dark. The thickness of these two lines will be quite different. Measure the resistance of each line. The thicker, darker line has a larger cross-sectional area, and should have a lower resistance than the lightly drawn line.
2. Draw a dark line 3-mm wide and 5-cm long. Place the probes from the meter very close together near the end of the line, and read the resistance on the meter. Now move the probes further apart and measure the resistance. Continue recording the resistance while using a ruler (or the graph paper squares) to measure the distance between the readings.
# of cm / 1 / 2 / 3 / 4 / 5
Plotting the data as a graph of resistance VS. distance. The resistance should increase linearly with the separation of the probes because the resistance is proportional in length. Therefore, a straight-line graph should result.
Now determine the slope of the line. Since R= L/A, the slope of a graph of R vs. L is /A.
C. The relationship between resistance and width.
3. Draw a line about 8-mm wide and 5-cm long. Draw a second line below it about 4-mm wide and 5-cm long. Below the second line draw a third line about 2-mm long and 5-cm long. Redraw the lines until they appear black. Try to keep the thickness of the lines comparable. Now place the contacts from the meter at the ends (5 cm apart) of the thin line and measure the resistance. Then place the contacts at the ends of the medium width line and measure the resistance. Finally, place the contacts at the ends of the wide line and measure the resistance.
# of cm / 8 / 4 / 2
What is the relationship between resistance and width? Plot another graph of Resistance VS. . Is the relationship linear? If not straighten the line by applying a formula to the data on one axis, then re-plot the graph. What is the slope of the line?
D. Resistance of Series Circuits
1. First draw a single resistor, which could be a straight line 3-mm wide and 5-cm long. Measure the resistance of the line. Across from and almost touching the first line, draw another resistor of similar dimensions, and measure its resistance. Now connect the two resistors (fill in the space between them). Measure the resistance across both resistors.
The resistance should equal the sum of the individual resistances. Mathematically, for two resistors in series,
R total = R1 + R2
Try drawing a circuit with 3 or more equivalent resistors in series. Measure the resistance of the first resistor (R1), the first and second resistors (R1+R2), and all three resistors (R1 + R2 + R3). Now plot these measured resistances versus the number of resistors measured. Note the linear dependence; the slope of the resulting line is R.
The relationship for resistors in series is that the total resistance is equal to the sum of the individual resistances. Note that the above equation is really just a restatement of the first equation. The resistance of a material is proportional to its length.
E. Resistance of Parallel Circuits
1. Draw two closely spaced, parallel lines of equal length, say 5-cm long and 5-mm wide. Measure and record the resistance of the first line (R1), then do the same with the second line (R2).
2. Now connect the ends of the two lines together and measure the resistance of the resulting parallel circuit (Rtotal).
3. Finally, fill in the remaining white space between the two lines, and measure the resistance of this single width line (Rwide).
The resistance should obey the standard rule for parallel resistors:
1/Rtotal = 1/R1 + 1/R2
Note that the relationship for resistors in parallel is the total resistance is inversely proportional to the cross sectional area of the resistor.