Electrical Conductivity of Graphite
Abstract
This experiment aims at examining the resistivity and hence conductivity of various ranges of
graphite pencils. This is achieved by first determining the resistance of the graphite pencils from
the current-voltage data. Resistivity is then determined from the calculated resistance values using
the equations defined in literature. Conductivity is also obtained by finding the inverse of
resistivity. The report further compares the resistivity of various ranges of graphite pencils with
the ideal resistivity of the pure graphite.
Objective
To examine the resistivity and conductivity of various ranges of graphite pencils.
Introduction
Resistivity is the characteristic property of a material to oppose the flow of current. It varies
depending on the nature of the material i.e. different materials have different resistivity. The
inverse of resistivity, otherwise known as conductivity, determines the ability of a material to carry
current. A direct proportionality relationship exists between resistance and resistivity as given by
𝑙
𝑅 = 𝜌𝐴
(1)
, 𝑤ℎ𝑒𝑟𝑒 𝜌 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦
𝑙 𝑖𝑠 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟
𝐴 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟
(Marcus and Marcus, 1974)
It can be deduced from equation (1) that the resistivity of a given material can be obtained from
its resistance provided the length and the cross-sectional are known.
This laboratory exercise exclusively focuses on the determination of resistivity and hence the
conductivity of various ranges of graphite. Graphite, an allotrope of Carbon, is a good conductor
of electricity. Pencil leads are usually made from a mixture of clay and graphite. However, clay is
not a good conductor of electricity. Its sole purpose in the pencils is to contribute to the hardness.
Different variations of pencils result from the content of clay used. Figure 1 shows the various
classifications of pencils based on the hardness (Mrozowski, 2017)
Figure 1: Variations of pencils based on the hardness
Materials







‘Lead’ pencils
Cables
GLX explorer
Voltage sensor
Current sensor
Probes
Power supply
Methodology
The experiment circuit was configured using the 4 probe configuration as shown in Figure 2 with
the initial voltage and current set to zero.
Figure 2: Wiring schematic for the 4-probe configuration
The voltage was then slowly increased while observing the current and voltage graph in
DataStudio. This was done till either a maximum current limit or a 2 V voltage was reached. The
measured current-voltage data were then recorded for various runs of graphite pencils.
A voltage versus current graph was then plotted and the resistance determined from the slope. The
resistivity and hence conductivity were then determined for each pencil using the obtained
resistance and the relation in (1).
Results
The resistance of each graphite pencil is obtained from the slope of the I-V characterisitics curves.
This is given by
𝑆𝑙𝑜𝑝𝑒 ⟹ 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =
△𝑉
△𝐼
(2)
With the resistance obtained from equation (2) and utilizing equation (1), the resistivity is
determined as follows
(3)
𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 =
𝐶𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑥 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟
The cross-sectional area of the graphite pencil is obtained from the diameter using the relation
𝐶𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎, 𝐴 = 𝜋
𝑑2
4
, 𝑤ℎ𝑒𝑟𝑒 𝑑 𝑖𝑠 𝑡ℎ𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ𝑖𝑡𝑒
It is obtained as underlisted for the various pencil ranges.
(4)
(i)
Figure 3 shows the voltage versus current characteristic curve for the pencil B as obtained from
the given data.
Pencil B
1,8
1,6
Voltage [V]
1,4
y = 1,6527x + 0,0125
1,2
1
0,8
0,6
0,4
0,2
0
0
0,2
0,4
0,6
0,8
1
Current [A]
Figure 3: Voltage-current characteristics of Pencil B
It is noted from the plot that the slope and hence the resistance of this kind of pencil is 1.6527
ohms. Given that the diameter of the pencil B is 2 [mm], its cross-sectional area is then obtained
from (4) as
𝐴=𝜋
(2 𝑥 10−3 )2
𝑑2
=𝜋
= 3.142 𝑥 10−6 𝑚2
4
4
With the provided data of the length and the calculated cross-sectional area of the pencil, its
resistivity is determined from equation (3) as
𝜌=
3.142 𝑥 10−6 𝑚2 𝑥 1.6527
= 4.71 𝑥 10−5 Ω ∙ 𝑚
110.25 𝑥 10−3 𝑚
𝜎=
1
= 21231.4 𝑆
𝜌
(ii)
Figure 4 shows the voltage againt current graph for this kind of pencil as obtained from the given
dataset.
Pencil 4B
0,7
0,6
y = 0,6102x + 0,0035
Voltage [V]
0,5
0,4
0,3
0,2
0,1
0
0
0,2
0,4
0,6
0,8
1
1,2
Current [A]
Figure 4: Voltage-current characteristics of Pencil 4B
It is noted from the plot that the slope and hence the resistance of this kind of pencil is 0.6102
ohms. Given that the diameter of this pencil is 2 [mm], its cross-sectional area is obtained from
(4) as
𝐴=𝜋
(2 𝑥 10−3 )2
𝑑2
=𝜋
= 3.142 𝑥 10−6 𝑚2
4
4
With the provided data of its length and the calculated cross-sectional area, the resistivity of this
pencil is determined from equation (3) as
𝜌=
3.142 𝑥 10−6 𝑚2 𝑥 0.6102
= 2.044 𝑥 10−5 Ω ∙ 𝑚
93.8 𝑥 10−3 𝑚
𝜎=
1
= 48923.679 𝑆
𝜌
(iii)
Figure 5 shows the voltage versus current characteristic curve for the pencil 2B as obtained from
the given dataset.
Pencil 2B
1,4
1,2
y = 1,168x + 0,0053
Voltage [V]
1
0,8
0,6
0,4
0,2
0
0
0,2
0,4
0,6
0,8
1
1,2
Current [A]
Figure 5: Voltage-current characteristics of Pencil 2B
It is noted from the plot that the slope and hence the resistance of this kind of pencil is 1.168
ohms. Given that the diameter of the 2B pencil is 2 [mm], its cross-sectional area is then obtained
from (4) as
𝐴=𝜋
(2 𝑥 10−3 )2
𝑑2
=𝜋
= 3.142 𝑥 10−6 𝑚2
4
4
With the provided data of the length and the calculated cross-sectional area of the pencil, its
resistivity is determined from equation (3) as
𝜌=
3.142 𝑥 10−6 𝑚2 𝑥 1.168
= 3.551 𝑥 10−5 Ω ∙ 𝑚
103.35 𝑥 10−3 𝑚
𝜎=
1
= 28161.081 𝑆
𝜌
(iv)
Figure 6 shows the voltage versus current characteristic curve for the F pencil as obtained from
the given dataset.
Voltage [V]
Pencil F
2
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
0,00E+00
y = 1,9513x + 0,0111
2,00E-01
4,00E-01
6,00E-01
8,00E-01
1,00E+00
Current [A]
Figure 6: Voltage-current characteristics of Pencil F
It is noted from the plot that the slope and hence the resistance of this kind of pencil is 1.9513
ohms. Given that the diameter of the F pencil is 2 [mm], its cross-sectional area is then obtained
from (4) as
𝐴=𝜋
(2 𝑥 10−3 )2
𝑑2
=𝜋
= 3.142 𝑥 10−6 𝑚2
4
4
With the provided data of the length and the calculated cross-sectional area of the pencil, its
resistivity is determined from equation (3) as
𝜌=
3.142 𝑥 10−6 𝑚2 𝑥 1.9513
= 4.478 𝑥 10−5 Ω ∙ 𝑚
136.9 𝑥 10−3 𝑚
𝜎=
1
= 22331.4 𝑆
𝜌
(v)
Figure 7 shows the voltage versus current characteristic curve for the 2F pencil as obtained from
the given dataset.
Pencil 2F
1,6
y = 1,5162x + 0,0071
1,4
Voltage [V]
1,2
1
0,8
0,6
0,4
0,2
0
0
0,2
0,4
0,6
0,8
1
Current [A]
Figure 7: Voltage-current characteristics of Pencil 2F
It is noted from the plot that the slope and hence the resistance of this kind of pencil is 1.5162
ohms. Given that the diameter of the 2F pencil is 2 [mm], its cross-sectional area is then obtained
from (4) as
𝐴=𝜋
(2 𝑥 10−3 )2
𝑑2
=𝜋
= 3.142 𝑥 10−6 𝑚2
4
4
With the provided data of the length and the calculated cross-sectional area of the pencil, its
resistivity is determined from equation (3) as
𝜌=
3.142 𝑥 10−6 𝑚2 𝑥 1.5162
= 3.5605 𝑥 10−5 Ω ∙ 𝑚
133.8 𝑥 10−3 𝑚
𝜎=
1
= 28085.94 𝑆
𝜌
(vi)
Figure 8 shows the voltage versus current characteristic curve for the HB pencil as obtained from
the given dataset.
Voltage [V]
Pencil HB
2
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
y = 2,1379x + 0,0115
0
0,2
0,4
0,6
0,8
1
Current [A]
Figure 8: Voltage-current characteristics of Pencil HB
It is noted from the plot that the slope and hence the resistance of this kind of pencil is 2.1379
ohms. Given that the diameter of the HB pencil is 2 [mm], its cross-sectional area is then obtained
from (4) as
(2 𝑥 10−3 )2
𝑑2
𝐴=𝜋
=𝜋
= 3.142 𝑥 10−6 𝑚2
4
4
With the provided data of the length and the calculated cross-sectional area of the pencil, its
resistivity is determined from equation (3) as
3.142 𝑥 10−6 𝑚2 𝑥 2.1379
𝜌=
= 6.7409 𝑥 10−5 Ω ∙ 𝑚
99.65 𝑥 10−3 𝑚
𝜎=
1
= 14834.814 𝑆
𝜌
Discussion
As observed from the obtained resistivity results of various ranges of graphite pencils, it is noted
that resistivity of particular materials is nearly constant regardless of the dimensions of the
conductor. It is however noted that for graphite pencils, resistivity slightly vary depending on the
level of hardness of the pencil. It is noted that resistivity slightly increases with increase in clay
content of the pencil. All the experimentally obtained resistivities are noted to nearly conform to
the resistivity of pure graphite which is approximately 1.38 𝑥 10−5 Ω ∙ 𝑚. (Parsons et al., 2001)
Negligible discrepancies were however noted to exist between the experimental and the theoritical
results. These differences can be attributed to various sources of experimental errors and
uncertainties. Possible sources of variations include temperature fluctuations. Although it was
assumed that the temperature of the room in which the experiment was conducted was constant, it
may have not been the case. The accuracy of the obtained results may have been compromised due
to the temperature dependence of resistivity (Griffith and Gayley, 2018). Other possible sources of
error may include the systemic errors emanating from the use of defective equipment as well as
the parallel error resulting from poor positioning of the eye when taking the readings.
Conclusion
In conclusion, the experimental circuit was configured and the desired data collected in line with
the stipulated procedure. These data were then analyzed accordingly to obtain the resistance,
resistivity and conductivity of various ranges of graphite. It was noted that the resistivity and hence
conductivity of graphite vary depending on the clay content; however, the value still conforms to
the theoretical values in literature. As all the objectives were accomplished, the laboratory exercise
was hence correctly carried out.
References
Griffith, O. and Gayley, R., 2018. The temperature dependence of the electrical resistivity of soft carbon
below 4.2°K. Carbon, 3(4), pp.541-542.
Marcus, A. and Marcus, W., 1974. Basic electricity. Englewood Cliffs, N.J.: Prentice-Hall.
Mrozowski, S., 2017. Electric Resistivity of Polycrystalline Graphite and Carbons. Physical Review, 77(6),
pp.838-838.
Parsons, A., Baker, W., Haslam, A., Barnes, J., Chaldecott, J. and Peacock, G., 2001. Electricity. Princeton,
N.J.: Two-Can Pub.