An Investigation of
the Resistivity of
Charcoal
Presented by: Si Hongbo
Lin Siqi
Wang Chengxu
Arun Balasubramaniam
Resistivity
• Electrical resistivity (also known as specific electrical resistance)
is a measure of how strongly a material opposes the flow of
electric current.
l
R
A
• where
http://en.wikipedia.org/wiki/Image:Resistivity_geometry.png
– ρ/ Ωm, is the resistivity
– R/ Ω, is the electrical resistance of a uniform specimen of the
material
– l/m, is the length of the specimen
– A/m², is the cross-sectional area of the specimen
Theories & Principles
• Ohm’s Law:
V
R
I
• where I is the current, V is the potential difference,
and R is a constant called the resistance
• Resistivity equation:
l
R
A
Hypothesis
• Charcoal sticks are not made of pure carbon, but
mixed with soil.
• Hence, the resistivity measured would be higher than
the resistivity of pure carbon
• Resistivity of carbon is about 3.5×10-5 Ωm
• Therefore, I hypothesize that the resistivity of charcoal
would be larger than the conventional resistivity of
carbon.
Objective & Setups
• To investigate the resistivity of charcoal.
• 6 thin charcoal sticks with the same diameter but
different lengths
Procedure
•
Measuring the length of the charcoal stick.
•
Adjust the rheostat to the highest resistance. Close
the switch.
•
Adjust the rheostat to certain extent, and record
down the voltage V and ampere A shown.
•
Calculate the resistance values using Ohm’s Law.
•
Plot a graph of lnR vs. lnl. Determine the average
resistivity of charcoal.
Results & Data
Cross-sectional area = 0.00005 m²
S/N l/m
V/V
R/Ω
I/A
V1
V2
V3
I1
1
0.01 0.4
0.5
0.6
8.2
2
0.02 0.4
0.5
0.6
3
0.03 0.4
0.5
4
0.04 0.4
5
6
I2
I3
R1
R2
R3
Rave
10.0 11.6 0.048
0.050
0.052
0.050
4.1
4.9
5.7
0.098
0.102
0.105
0.102
0.6
2.8
3.3
3.8
0.143
0.152
0.158
0.151
0.5
0.6
2.1
2.4
2.8
0.190
0.208
0.214
0.204
0.05 0.4
0.5
0.6
1.7
1.9
2.2
0.235
0.263
0.273
0.257
0.06 0.4
0.5
0.6
1.2
1.5
1.7
0.333
0.333
0.353
0.340
Results & Analysis
lnA = -9.9
lnR
-3.00
-2.28
-1.89
-1.59
-1.36
-1.08
lnl
-4.61
-3.91
-3.51
-3.22
-3.00
-2.81
l
R 
A
l 

ln R  ln   
 A
ln R  ln l  ln   ln A
Plot a graph of lnR vs. lnl, so the y-intercept is
ln   ln A
Results & Graph
Plot a graph of lnR vs. lnl
Graph of lnR vs. lnl
-4
-3
-2
lnR
-5
0
-1 -0.5 0
-1
-1.5
-2
-2.5
-3
-3.5
lnl
lnl
We can get the y-intercept to be (0 , 1.65), which is
ln   ln A  1.65
  0.00026 2.6 104   m
Conclusion
• We have gotten the experimental value of the
resistivity of charcoal, which is about 2.6 x 10-4 Ωm.
• The value is larger than the resistivity of carbon, but
still very low.
• The hypothesis is accepted. The objective is fulfilled.
Precautions
• Experimental precautions:
• Charcoal sticks: homogeneous
• Temperature
• rheostat adjustment
• Safety precautions:
• keep the voltage within a safety range
• To protect the ammeter and voltmeter
Evaluation
• Assumptions:
• There is no temperature change.
• The charcoal sticks are in regular shape and are thin
cylinders.
• The charcoal sticks are homogeneous: the percentage
of carbon and soil is consistent for all 6 sticks. The
carbon and soil are evenly dispersed.
Evaluation
• Assumptions:
• The resistance of the voltmeter is extremely large,
since its resistance would affect the ampere values
recorded.
• The experiment is done under constant voltage, since
the power supply may work inconsistently.
Evaluation
• Error sources:
• Temperature changes affect the resistances of most
conductors, since the speed of the delocalized
electrons or ions varies with temperature.
• High voltage and current cause more heat, due to
Joule’s Law:
2
V
Q  I Rt 
t
R
2
• Inconsistent voltage supply
Evaluation
• Improvement & Extension:
• To use electronic multi-meters, which can measure the
variables more accurately, instead of classical
mechanical ammeters and voltmeters.
• To get a better and more consistent power supply.
• To get purer charcoal, so that eventually we can
measure the resistivity of carbon approximately.
Evaluation
• Personal Comments:
• This is the 1st experiment on electricity we have ever
carried out since last year.
• Experiments (high school level) on electricity &
magnetism are relatively easier to conduct. The
results are easier to recorded.
• From this experiment, we revised the knowledge on
resistance, and its related matters.