INVESTIGATING THE RESISTIVITY OF A WIRE
Electrical resistance is a physical quantity characterizing the properties of the conductor to interfere with the passage of electric current and voltage, which is equal to the ratio of the voltage at the end of the conductor to the current flowing through it (Brown, Forbes T., 2006, p. 43).
The electrical resistivity is a physical value that characterizes the ability of a substance to prevent the passage of electric current.
The resistance of an electrical circuit can be calculated, with the help of two equations below (Woan, G., 2010).
R – Resistance (ohms), V – Voltage (volts), I – Current (amps)
p – Resistivity (ohm.m)
L – Length (meters)
A – Cross-sectional area (meters2)
A physical meaning of resistivity is that it is a resistance of homogeneous conductor made of the given material of length of one unit and of cross-sectional area of one unit (Laughton, M. A.; Warne, D. F., 2003, p. 10).
Constantan is a copper-nickel alloy consisting of 55% copper and 45% nickel. It is famous for its resistivity, which is constant over a wide range of temperatures (Davis, J. R., 2001, p. 158.). The resistivity of the constantan wire id 49x10-8 Ω.m.
Objective: to determine the resistivity of a constantan wire.
Hypothesis: resistivity depends only on the material of the wire and does not depends on its thickness.
Calculation of Cross sectional Area of thick Wire:
Calculation of Cross sectional area of thin Wire:
Average Value of Resistivity:
Average Value of Resistivity:
Results and discussion
Calculated (average) resistivity of thick wire: 4.551 x 10-7 Ω.m
Calculated (average) resistivity of thin wire: 4.115 x 10-7 Ω.m
Resistivity of thick wire obtained from the graph: 4.968 x 10-7 Ω.m
Resistivity of thin wire obtained from the graph: 4.188 10-7 Ω.m
Both of obtained graphs are mostly linear. Calculation of a gradient a linear approximation was performed with the help of MS Excel’s trend line. Gradient is a tangent of angle between X-axis and a trend line.
Theoretical and experimental values of resistivity are very close for both thick and thin wire. Relative deviation of the values for thick wire is 9.2% and for thin wire is 1.8%.
Two graphs look quite similar.
The experiment can be improved by more accurate measurements and enhancing number of experiments. Calculations of average values may become more precise if the researcher will not be taking into consideration those few marks on the graph that are too far of trend line.
It is necessary to be very careful while working in the laboratory with electric measuring devices. In case of equipment malfunction or a bad condition of wires, it is very important to report to instructor and not to touch anything that might be dangerous. It is absolutely prohibited to try to fix broken equipment. After the end of work, all devices should be switched off. Person, working in the laboratory, should know rules of first aid.
The hypothesis was proven in the process of carrying out the experiment. Resistivity does not depend on wire thickness and its length and depends only on its material. As both wires used in the work were constantan ones the values of resistivity obtained during both experiment and calculations were very similar. As known resistivity of constantan wire is 4.9 x 10-7 Ω.m, the obtained values are very close. Relative deviation ranges from 1.4 % to 16.0 %. Both obtained graphs are linear because of the linear relationship between resistance and length/area values. I have learnt from the experiment that for the same material resistivity is a constant value. Any possible errors in this work could have come from inaccurate measurements and calculation errors.
Brown, Forbes T. 2006. Engineering System Dynamics. CRC Press. p. 43.
Davis, J. R. 2001. Copper and Copper Alloys. ASM International. p. 158.
Laughton, M. A.; Warne, D. F. 2003. Electrical Engineers Reference Book (16th ed.). Elsevier. p. 10/43.
Woan, G. 2010 The Cambridge Handbook of Physics Formulas. Cambridge University Press.