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 resistanc

e) is a measure of how strongly a material opposes the flow of electric current.

• where– 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

A

lR

http://en.wikipedia.org/wiki/Image:Resistivity_geometry.png

Theories & Principles• Ohm’s Law:

• where I is the current, V is the potential difference, and R is a constant called the resistance

• Resistivity equation:

I

VR

A

lR

Hypothesis• Charcoal sticks are not made of pure carbon, but mixe

d 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

S/N l/mV/V I/A R/Ω

V1 V2 V3 I1 I2 I3 R1 R2 R3 Rave

1 0.01 0.4 0.5 0.6 8.2 10.0 11.6 0.048 0.050 0.052 0.050

2 0.02 0.4 0.5 0.6 4.1 4.9 5.7 0.098 0.102 0.105 0.102

3 0.03 0.4 0.5 0.6 2.8 3.3 3.8 0.143 0.152 0.158 0.151

4 0.04 0.4 0.5 0.6 2.1 2.4 2.8 0.190 0.208 0.214 0.204

5 0.05 0.4 0.5 0.6 1.7 1.9 2.2 0.235 0.263 0.273 0.257

6 0.06 0.4 0.5 0.6 1.2 1.5 1.7 0.333 0.333 0.353 0.340

Cross-sectional area = 0.00005 m²

Results & Analysis

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

A

lR lnln

A

lR AlR lnlnlnln

lnA = -9.9

Plot a graph of lnR vs. lnl, so the y-intercept is

Alnln

Results & Graph

Graph of l nR vs. l nl

- 3. 5- 3

- 2. 5- 2

- 1. 5- 1

- 0. 50

- 5 - 4 - 3 - 2 - 1 0

l nl

lnR l nl

m 4106.200026.0

Plot a graph of lnR vs. lnl

We can get the y-intercept to be (0 , 1.65), which is

65.1lnln A

Conclusion• We have gotten the experimental value of the resistivit

y 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:

• Inconsistent voltage supply

tR

VRtIQ

22

Evaluation• Improvement & Extension:• To use electronic multi-meters, which can measure th

e 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.