TABLE OF CONTENTS

Title page

Certification

Dedication

Acknowledgements

Table of content

CHAPTER ONE

1.0     Introduction

CHAPTER TWO

2.0     Concept of Resistivity

2.1     Relation to Resistivity and Conductivity

2.2     Measurement of Resistivity

2.3     Static and Different Resistance

2.4     Electrical Resistance and Conductance

CHAPTER THREE

3.0     Simple model and theory of resistivity

3.1     Importance of Resistivity

3.2     Ohmic and Non-Ohmic Resistance

CHAPTER FOUR

4.0     Summary and Conclusion

4.1     Summary of Resistivity

4.2     Conclusion

References

CHAPTER ONE

1.0 Introduction

Electrical resistivity (also known as resistivity, specific electrical resistance, or volume resistivity) is a measure of how strongly a material opposes the flow of electric current. A loss resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm.meter (.m). it is commonly represented by the Greek letter p (rho) (Wieder, 2021).

Electrical resistivity p (Greek: rho) is defined by,

P = E –        –         –         –         –         –         -1.1

J

Where p is the static resistivity of the conductor material (measured in ohm.meters, MΩ.m), E is the magnitude of the electric field (in volts per metre, V.M^-1), J is the magnitude of the current density (in amperes per square metre, A.M^-2) in which E and J are inside the conductor.

Conductivity is the inverse of resistivity:

= I  –         –         –         –         –         –         –         1.2

P

 Which gives an equivalent equation:

= J  –         –         –         –         –         –         –         1.3

E

As the matter of fact, some resistors and conductors have a uniform cross section with a uniform electric flux (Maissel, 2003). They are composed of one material normally as shown above. In this case, the above definition of p leads to:

P = RA –      –         –         –         –         –         –         1.4

L

Where:

R- is the electrical resistance of a uniform specimen of the material (measured in ohms, )

ɩ is the length of the piece of material (measured in meters, m)

a is the cross-sectional area of the specimen (measured in square meters, M²).

The reason resistivity has the dimension units of ohm.meters can be  seen by transposing the definition to make resistance the subject (Pouillet’s law):

R = p e –      –         –         –         –         –         –         –         1.5

A

The resistance of a given sample increases with the length, but decreases with greater cross- sectional area. (Wieder, 2001).

Resistance is measured in ohms. Length over area has unit of 1/distance. To end up with ohms, resistivity must be in the units of “ohms x distance” (SI ohm.meter, US ohm.inch).

In a hydraulic analogy, increasing the cross- sectional area of a pipe reduces its resistance to flow, and increasing the length increases resistance to flow (and pressure drop for a given flow). (Zhai et al., 2018).