CHAPTER ONE

1.0 INTRODUCTION

1.1 BACKGROUND OF STUDY

In the context of high metal prices particularly of copper; the main material used in electrical conductors, a reduction in the use of raw materials is one of the challenges facing the cable industry today. Thus the usage of copper or aluminium (or any other conducting material) in the manufacturing of cables must be analysed to achieve the desired electrical conductance under the imposed conditions. This paper presents partial results of our work concerning the development of a finite element model for three-dimensional modelling and design optimization of multi-strand conductors. One of the points hindering this study has been the lack of understanding in the area of contact between wires. Indeed, these areas of contact between the wires of the cable, are an essential problem for a model incorporating robust mechanical and electrical coupling. The characteristics of the contact electrical parameters between the conductor strands versus mechanical stress and the relative position of individual wires have a significant influence on the distribution of current lines in the cable. This paper is focused on the characterization of the electrical contact resistance by experimental measurements and electromechanical simulation based on the finite element method. The authors’ interest mainly focuses on the study of electrical Cu/Cu contact between two conductors under the influence of a compressive force. The attention is particularly concentrated on the study of the influence of the contact force and of the crossing angle between the wires, and the shape and the size of the contact area. In the first phase, the experimental measurement device was prepared. First the bench for applying compression and measurement of the contact force was built. It also has a system for fixing the angle of intersection of the conductors. Measurements have been conducted for DC loads. The electrical contact resistance, for its part, is measured using a 4-pointmethod (Kelvin method) with amicro-ohmmeter. The measurement protocol and the experimental test conditions are specified. In a second step, the results of several dozen tests are presented. The analysis of these results is performed in order to understand the influence and quantify the impact of each factor studied on the electrical behaviour of the contact interface, including its resistance. After each measurement the sample was examined under a microscope to first investigate the shape and the size of the imprint, and second to investigate the internal structure of the conductor. The copper wires from which the measured samples have been made are produced using a process called cold deformation. The stranding and compacting process is a complex operation that combines two simultaneous displacements: translation and rotation. From these combined displacements, three distinct forces will act on the wires: traction, torsion and compression. To compare the measurement and simulation results, this process was modelled using the Abaqus program  which allows simulating the stranding and compacting operation to calculate the mechanical deformations, the residual stresses, the inter-strands contact pressure and the resultant plastic strain. This program detects the contact zone as well as calculates the stress distribution. Thanks to the measured characteristics of the resistivity as a function of stress it is possible to takes into consideration the non-homogenous resistivity of the contact zone. The non-homogenous resistivity will be implemented and taken into account in the finite elements model by defining an electromechanical coupling strategy. This will allow us to perform a more detailed analysis of the electrical phenomena and their impact on the total electrical resistance of the conductive core

1.2 STATEMENT OF PROBLEM

What really instigated the study on the effect of length on the resistance of copper wire was due to variation in the result of various experiments conducted on copper wires. Secondly there have been series of studies on Ohm’s law but not even a single study has tried to verify ohm’s law for the effect of length on the resistance of copper in Nigeria

1.3 AIM AND OBJECIVES OF STUDY

The main aim of the research work is to determine the effect of length on the resistance of a copper wire. Other specific objectives of the study are:

1. to determine the effect of length of copper wire on the current flow
2. to investigate on the factors affecting the resistance of copper wire
3. to verify Ohm’s Law for series and parallel circuits
4. to examine the conductivity and resistivity of copper wire

1.4 RESEARCH QUESTIONS

The study came up with research questions so as to ascertain the above stated objectives of the study. The research questions for the study are:

1. What is the effect of length of copper wire on the current flow?
2. What are the factors affecting the resistance of copper wire?
3. Is the verification of Ohm’s Law for series and parallel circuits effective?
4. What is the conductivity and resistivity of copper wire?

1.5 SIGNIFICANCE OF STUDY

The study on the effect of length on the resistance of a copper wire will be of immense benefit to the physics department because it will help the students gain a better understanding on ohm’s law, the study will also show in an experiment the relationship between the length of copper wire and the resistance to the flow of current. The study will also serve as a repository of information to other researchers that desire to carry out similar research on the above topic. Finally the study will contribute to the body of existing literature and knowledge in this field of study and provide a basis for further research

1.6 SCOPE OF STUDY

The study on the effect of length on the resistance of a copper wire will cover on resistance, the effect of the length of copper wire on current flow and finally the study will also cover on the effect of length on the resistance of a copper wire.

1.7 DEFINITION OF TERMS

Electrical resistance: The electrical resistance of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor

Electric Current: An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire

Voltage: Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points

Resistors: A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element.