# RESISTIVITY: ITS CONCEPT AND IMPORTANCE

**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, M^{2}).

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).