Lab
Resistance and Resistivity
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Purpose
This lab was adapted from the lab entitled "
Using Graphite Paper to prove the relationship of R =
ρ
L/A
" hosted by the website
prettygoodphysics
. It was posted by Jennifer Groppe on Feb 27, 2010. She based her version on an article from
The Physics Teacher
. The lab's purpose is to examine how the geometry of a rectangular conductor affects its resistance.
Equipment
ohm-meter (k
Ω)
conductive paper
scissors
EXCEL
Part I - Reduction of Area
1. Cut the border off of the conductive paper so that you have a grid that is 20 by 25 blocks.
2. Cut this grid down to two pieces that are each 10 by 25 blocks.
3. Measure the resistance of the piece of paper lengthwise, placing the multimeter probes in the center of the paper. Record this value in the table below making sure that the mater is set to k
Ω
. When the paper is very wide, the reading may fluctuate a lot---just try to pick an average reading.
4. Cut a single LONG strip (not short) off of the conducting paper along the grid markings. This will leave you with a sheet of paper that is 8 rows by 25 columns. Measure the resistance of the remaining paper as you did above - always making sure that you place the probes at the middle of the edge of each end as shown below.
5. Repeat this procedure, cutting off one row at a time, until you have ten identical strips of conducting strips of
paper that are 1 row high by 25 columns long.
Record your readings in the table provided below. Then plot in EXCEL a graph of Resistance vs Area. Save your EXCEL file as ResistivityLastnameLastname.xlsx
Refer to the following information for the next ten questions.
Resistance readings for Part I - Reduction of Area.
number of
area
resistance
trial
rows
(m
^{2}
)
(ohms)
1
2
3
4
5
6
7
8
9
10
Which of the following correctly describe the shape of your graph in EXCEL?
linear
hyperbolic (power -1)
parabolic (power 2)
no pattern - random scattering
What was the leading coefficient of your graph's trend line?
What was the R
^{2}
, correlation coefficient, of your trend line?
Refer to the following information for the next two questions.
Conclusions for Part I
How did the resistance of the paper change as you decreased its width? BE specific. (it increased slowly, then quickly; it decreased at a uniform rate; it did not change)
Explain why the removal of the last strip has a greater effect than the removal of the first strip. Hint—think of percentages. Be specific and accurate.
Part II - Increasing the Cross-Sectional Area
1. Measure the resistance of ONE of your 10 strips of paper. Record this value in the next table. Your multimeter should still be set to k
Ω
.
2. Place a second strip directly on top of the first strip. Measure the resistance of the new arrangement and record this value in the following table.
3. Repeat this procedure until you have a stack of 10 strips.
4. Then plot in EXCEL a graph of Resistance vs Stack of Strips. Resave EXCEL.
Refer to the following information for the next ten questions.
Resistance Readings for Part II - Increasing the Cross-Sectional Area.
number of
resistance
strips
(ohms)
1
2
3
4
5
6
7
8
9
10
Which of the following correctly describe the shape of your graph in EXCEL?
linear
hyperbolic (power -1)
parabolic (power 2)
no pattern - random scattering
What was the R
^{2}
, correlation coefficient, of your trend line?
Refer to the following information for the next three questions.
Conclusions for Part II
What happened to the total resistance as the stack became taller? Be specific. (it increased at a uniform rate; it decreased quickly than slowly, etc.)
Compare your results for procedures I and II. Calculate the percent difference in the resistance for 3 strips stacked to 3 strips side by side.
Based on your measurements, does it matter whether the surface area is wide but not tall or tall but not wide? Support your answer.
Part III: Decreasing the length of the conductor.
1. Take ONE STRIP and measure the resistance from end to end. Remember to place the probes in the center of the strip and keep your ohm-meter in k
Ω
. Record your values in the table below.
2. Next cut off FIVE of the 25 grids, and measure the resistance of the remaining strip. Your strip will have a length of 20 grids by a height of 1 row.
3. Next cut off FIVE more of the 20 grids, and measure the resistance of the remaining strip. Your strip will have a length of 15 grids by a height of 1 row.
4. Repeat this process, cutting off FIVE strips each time until there are no grids left.
5. Then, take one of the remaining five strips by 1 row and cut off 1 grid at a time - from 5 to 4 to 3 to 2 to 1.
6. Then plot in EXCEL a graph of Resistance vs Strip Length. Resave EXCEL.
Refer to the following information for the next nine questions.
Resistance Readings for Part III - Decreasing the Length of the Conductor
length
length
resistance
(grids)
(m)
(ohms)
25
20
15
10
5
4
3
2
1
Which of the following correctly describe the shape of your graph in EXCEL?
linear
hyperbolic (power -1)
parabolic (power 2)
no pattern - random scattering
What was the R
^{2}
, correlation coefficient, of your trend line?
Refer to the following information for the next five questions.
Conclusions for Part III.
What happened to the resistance of the paper as you decreased its length? Be specific. (it increased at a uniform rate, it increased quickly, then slowly, etc.)
What is the thickness of the conducting paper? (in meters)
What is the width of the conducting paper in Part III? (in meters)
What is the area of the conducting paper in Part III? (in square meters)
Using the slope of the trend line from Part III, calculate the resistivity of the conducting paper.
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