1. An Investigation of the Resistivity of Charcoal Presented by: Si Hongbo Lin Siqi Wang Chengxu Arun Balasubramaniam

2. Resistivity Electrical resistivity (also known as specific electrical resistance) 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 http://en.wikipedia.org/wiki/Image:Resistivity_geometry.png

3. 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:

4. 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.

5. Objective & Setups To investigate the resistivity of charcoal. 6 thin charcoal sticks with the same diameter but different lengths

6. 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. ln l. Determine the average resistivity of charcoal.

7. Results & Data S/Nl/m V/VI/AR/Ω V1V1 V2V2 V3V3 I1I1 I2I2 I3I3 R1R1 R2R2 R3R3 R ave 10.010.40.50.68.210.011.60.0480.0500.0520.050 20.020.40.50.64.14.95.70.0980.1020.1050.102 30.030.40.50.62.83.33.80.1430.1520.1580.151 40.040.40.50.62.12.42.80.1900.2080.2140.204 50.050.40.50.61.71.92.20.2350.2630.2730.257 60.060.40.50.61.21.51.70.333 0.3530.340 Cross-sectional area = 0.00005 m²

8. 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 lnA = -9.9 Plot a graph of lnR vs. ln l, so the y-intercept is

9. Results & Graph Plot a graph of lnR vs. ln l We can get the y-intercept to be (0, 1.65), which is

10. 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.

11. Precautions Experimental precautions: Charcoal sticks: homogeneous Temperature rheostat adjustment Safety precautions: keep the voltage within a safety range To protect the ammeter and voltmeter

12. 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.

13. 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.

14. 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

15. 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.

16. Evaluation Personal Comments: This is the 1 st 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.