## Introduction

Resistivity is a parameter which defines the resistance of a metal to the flow of electric current per unit volume of the metal (Jones, n.d.). The resistivity exhibited by a metal is dependent on three physical properties; the cross-sectional area, length, and the nature of the material (A´ ngel & Tirado-Miranda, 2009). The value of resistivity dictates the conductivity of a metal, high resistivity is associated with low electrical conductivity while low resistivity means that the metal is a good conductor (The Physics Hypertext Book, n.d.). Therefore, it can be concluded that low resistivity allows for increased movements of electrons within the metal while high resistivity impedes the electron flow (Wissmann & Finzel, 2007).

Resistivity can be derived from the current density J, and the electric field E. These two parameters can be presented as;

J=σE equation 1.

## Where σ is the conductivity of the metal (Dyos & Farrell, 1992).

Conventionally, the resistance of a conductor increases with increase in length and decrease with increase in cross-sectional area (Poole, n.d.). This relationship can be represented as;

## RαL and Rα1/A. Therefore;

R=L/Aσ equation 2.

## But resistivity is the opposite of conductivity, therefore;

σ=1/ρ equation 3.

Where ρ is the resistivity of the metal (The Engineering Toolbox, n.d.)

## Equation 2 can therefore be rewritten as:

R=(ρL)/A equation 4.

## Hence;

ρ=RA/L equation 5 (Stack Exchange, n.d.)

Apart from the nature of a material, resistivity is also influenced by two other factors, impurities and temperature conditions. Impurities affect the number of free electrons responsible for electricity conduction in a metal. A high concentration of impurities considerably lower the number of electron per unit volume of the metal and a result lower amounts of current can flow through the metal for a given electrical potential. In non-metals such as silicon, impurities have been used to create semi-conductors. Impurities such as boron are added to non-metals in a process called doping whereby electrons from the doping element are added to the electron structure of the substrate material resulting to extra electrons which are free for electrical conduction. In this case, addition of materials through doping reduces the resistivity of the material (Jones, n.d.).

Rise in temperature have been known to increase the resistivity of material especially metals. This is because increase in temperature causes the free electrons to vibrate and collide with each other. When the electrons collide, they lose energy gained from the electrical potential and hence increase in resistance and thus the resistivity. The increase in resistance is proportional to rise in temperature.

## Considering a fractional change in temperature, the resulting resistance can be denoted as:

dTα=dR/Rs equation 6.

Where dR is the change in resistance, Rs the standard resistance, α the coefficient of temperature resistance, and dT the change in temperature.

## Equation 6 above can be modified to:

dR=αdTRs equation 7 (The Engineering Toolbox, n.d.).

An experiment was carried out to investigate the relationship between resistance, length, and cross-sectional area. Copper and nichrome wires of 1.2mm diameter and varying lengths were used.

## Aim

The aim of the experiment was to determine the resistivity of copper through the evaluation of variation of resistance with length and cross-section-area of a copper wire.

## Materials

The materials used in the resistivity experiment included nichrome and copper wires, micrometer screw gauge, masking tape, and crocodile clips.

Risk Assessment

The equipment used to conduct the experiment posed a considerable risk of electric shock to the users. To ensure against this, thick soled rubber shoes were worn to minimize conductivity and exposure. Also, conductive materials such as metals were cleared from the bench during the experiment. Measures were also taken to ensure that naked parts of the wire under investigation did not come into contact with exposed body parts such as hands as the experiment was being conducted.

## Hypothesis

If the cross-section area is held constant, it is expected that the resistance should increase with increase in length (Hyperphysics, n.d.). When the length is held constant and the cross-section area is altered, the resistance is expected to increase when the area is decreased (Solecon Labs Inc, n.d). Conversely, an increase in the cross-section area will lower the resistance of the wire (Schoolscience.co.uk, n.d.). The experiment was intended to prove this through the use of copper and nichrome wire strips of different lengths. Wires of 1.2mm diameter were used to observe the change in resistance among wire samples of different lengths.

## References

Wissmann, P., & Finzel, H.-U. (2007). Electrical resistivity of thin metal films. Berlin: Springer.

Dyos, G. T., & Farrell, T. (1992). Electrical resistivity handbook. London, U.K: Peter Peregrinus on behalf of the Institution of Electrical Engineers.

Poole, I. (n.d.). Electrical Resistivity: formula & units. Adrio Communications Ltd. Retrieved from http://www.radio-electronics.com/info/formulae/resistance/resistivity-basics- formula-equation-units.php

The Engineering Toolbox. (n.d.). Resistivity, Conductivity and Temperature Coefficients for some Common Materials. Retrieved from http://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html

Stack Exchange. (n.d.). Is it possible to mathematically derive the formula for resistance? Retrieved from http://physics.stackexchange.com/questions/23813/is-it-possible-to- mathematically-derive-the- formula-for-resistance

ChemWiki. (n.d.). Resistivity. UCDacis. Retrieved from http://chemwiki.ucdavis.edu/u_Materials/Electronic_Properties/Resistivity

Solecon Labs Inc. (n.d). Restivity. Retrieved from http://www.learnabout- electronics.org/Resistors/resistors_04.php

Bridge Technology. (n.d.). Understanding Volume Resistivity Measurements. Retrieved from http://four-point-probes.com/understanding-volume-resistivity-measurements/

A´ ngel, M. & Tirado-Miranda, M. (2009). A simpler derivation of the integral formula of electrical resistance. IOP Science. Retrieved from http://iopscience.iop.org/0143- 0807/30/4/L01

Hyperphysics. (n.d.). Resistivity and Temparature coefficient at 20C. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/tables/rstiv.html

Jones, G. (n.d.). Electrical resistivities. Kaye & Laby. Retrieved from http://www.kayelaby.npl.co.uk/general_physics/2_6/2_6_1.html

NDE-ED.org. (n.d.). Electrical Conductivity and Resistivity. Retrieved from https://www.nde- ed.org/EducationResources/CommunityCollege/Materials/Physical_Chemical/Electrical.htm.

Schoolscience.co.uk. (n.d.). Resistance and resistivity. Retrieved from http://resources.schoolscience.co.uk/CDA/16plus/copelech2pg1.html

Elert, G. (n.d.). Resistivity of Copper. The Physics Factbook. Retrieved from http://hypertextbook.com/facts/2004/BridgetRitter.shtml

The Physics Hypertext Book. (n.d.). Electric Resistance. Retrieved from http://physics.info/electric-resistance/