Resistivity of Metallic Wire
Experimental measurement of electrical resistivity of a metallic wire.
Resistivity is a very important property of materials. It determines usage of materials in different real life engineering applications. A material with low resistivity is suitable for application as electrical wires, while that with high resistivity is suitable for electrical insulation applications. Metallic materials, as a class of materials have low electrical resistivity because of presence of free electrons to conduct electrical energy under applied electrical potential or field and therefore, are good conductor of electricity. This is the reason why metallic wires are used for electrical transmission. Among metals also, there is variation from one metal to another. While copper, aluminum, gold, silver, molybdenum etc are very good conductors of electricity because of their low electrical resistivity (http://en.wikipedia.org/wiki/Electrical_resistivity); materials like steels and other engineering alloys have moderately high electrical resistivity.
Polymers and ceramics as a class of material have very high electrical resistivity. This is because these materials do not have free electrons to conduct electrical energy under applied electrical potential or field. Therefore, these materials are used as electrical insulators.
Resistivity in a material arises because of hindrance to the motion of charge carriers like electrons or ions, which tend to migrate under influence of the applied voltage. Resistivity of a material can be experimentally measured by measuring the electrical current under applied electrical potential and taking into consideration, the geometry of the sample. The underlying theory for such a measurement is discussed in the subsequent section. This paper presents the findings of experimental measurements of resistivity of a metallic wire.
All the conductors which obey Ohm’s law are called Ohmic conductors and for such conductors, the electrical current (I) is directly proportional to the applied voltage (V) in other words the ratio of the applied voltage to the electrical current (V/I), known as resistance (R) is independent of the applied voltage. Metallic wires are Ohmic conductors and therefore, for metallic wires the electrical resistance is independent of the applied voltage i.e.
is independent of the applied voltage V.
Resistance of a metallic wire is related to the electrical resistivity of the metallic material by the following equation (http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html).
where ‘r’ is resistivity of the material, ‘R’, ‘A’ and ‘L’ are respectively electrical resistance, area of the cross-section and length of the metallic wire.
From the experiment one can calculate V, I, A and L and then using the above two equations one can calculate resistivity of the metallic material.
Materials and Equipments
Metallic wires of diameter d = 2.86*10-4 m and different lengths 0.3 m, 0.4 m, 0.5 m, 0.6 m, 0.7 m, 0.8 m, 0.9 m and 1.0 m.
DC power supply, Ammeter, Voltmeter and Variable resistance.
The experimental set up prepared as in Fig. 1, below. The voltmeter was connected in parallel to the experimental wire for measuring potential difference across the electrical wire and the ammeter was connected in series to the measure the electrical current through the experimental wire. Variable resistance was used to set the potential difference across the experimental wire at different values and the corresponding electrical current through the experimental wire was measured in the ammeter. For a given length of experimental wire, electrical current was recorded for three different voltages. These experiments were repeated for wires of different lengths.
Fig. 1: Schematic of the experimental set up for resistivity measurement
Data and Calculations
The electrical current (I) and voltage (V) data as well as the calculated values of resistance (R) and resistivity (r) for different lengths of the metallic wire are presented in Table 1, below.
Table 1: Resistivity of metallic wire L (m) V 1 I 1 R 1 r 1 0.76 0.08 9.50 6.0990E-07 0.9 0.73 0.09 8.11 5.7859E-07 0.8 0.72 0.1 7.20 5.7780E-07 0.7 0.7 0.11 6.36 5.8364E-07 0.6 0.68 0.13 5.23 5.5969E-07 0.5 0.64 0.13 4.92 6.3212E-07 0.4 0.6 0.17 3.53 5.6647E-07 0.3 0.55 0.21 2.62 5.6048E-07 L (m) V 2 I 2 R 3 r 1 0.74 0.08 9.25 5.9385E-07 0.9 0.75 0.09 8.33 5.9444E-07 0.8 0.71 0.1 7.10 5.6978E-07 0.7 0.69 0.11 6.27 5.7530E-07 0.6 0.67 0.12 5.58 5.9742E-07 0.5 0.65 0.14 4.64 5.9614E-07 0.4 0.59 0.15 3.93 6.3130E-07 0.3 0.52 0.2 2.60 5.5640E-07 L (m) V 3 I 3 R 3 r 1 0.74 0.07 10.57 6.7869E-07 0.9 0.73 0.08 9.13 6.5092E-07 0.8 0.72 0.09 8.00 6.4200E-07 0.7 0.68 0.1 6.80 6.2366E-07 0.6 0.64 0.12 5.33 5.7067E-07 0.5 0.62 0.12 5.17 6.6340E-07 0.4 0.58 0.16 3.63 5.8181E-07 0.3 0.5 0.19 2.63 5.6316E-07 Average Resistivity 5.9823E-07
The calculation was done in MS Office Excel using the following formulae.
Area of cross-section A = 2*p*r2 = 2*3.14*(1.43*10-4)2 m2 = 6.42*10-8 m2
Average Resisitivity = 5.9823*10-7 Wm
Variation of Electrical resistance (R) with length of the electrical conductor (L) is presented in Fig.2, below.
From this figure, it is clear that electrical resistance of a metallic wire is linearly dependent on length of the wire as predicted by the governing equation. This confirms that experiment was conducted well and the results are in conformity with the theoretical predictions.
The experimental determination of electrical resistivity of the metallic wire has resulted in the value of electrical resistivity of 5.9823*10-7 Wm for the metallic material. There has been scatter in the experimentally measured values of the electrical resistivity of the metallic material from one experiment to another. Such scatter is natural and arise form errors in measurements of different experimentally measured values like voltage, current, length of the wire and diameter of the wire. Diameter of the wire has been taken as constant in these experiments, but there may be small variation in this value from one wire to another and this could be a possible source of the scatter in the experimentally measured values of the resistivity, besides the random errors from measurements of other variables.
The plot of electrical resistance vs. length of the wire (Fig. 2) is a straight line, as predicted by the theoretical relationship . This confirms that the experiment was carried out in a reasonably accurate manner.
The experimental measurements for the resistivity of the metallic wire have resulted in the value of the electrical resistivity r = 5.9823*10-7 Wm and the linear relationship between resistance and the length of the metallic wire confirms that the experiment was done in reasonably accurate manner.