Introduction

Resistance is the property of a body that opposes the passage of current. It is expressed in ohms and is written as an expression of current and voltage. The resistivity is the measure of the opposition of a material to the electrical current through it. 

What is resistance?

Resistance is the property of the materials that opposes the passage of electrical current through them. Based on resistance, materials are classified as resistors, insulators, and conductors.

Resistance of different materials

When comparing the resistance of the different materials, their resistivity is taken into consideration. Some of the materials and their associated resistivities at zero degrees Celsius are:

Conductors:

Alloys:

Semiconductors:

Insulators:

What is the resistivity formula?

The resistivity formula is:

ρ  = E /J 

where E is the electric field

J is the current density

R = ρ L/A

Where R is the resistance

L is the length of the conductor

A is the area of cross-section of the conductor

Resistivity unit

The CGS unit of resistivity is Ω.cm and the SI unit is Ω.m.

Relation between conductivity and resistivity

Conductivity is the measure of the current passing through a conductor per second or is the measure of the electrical ability of the conductor. It is represented by “σ “ and is pronounced “sigma.’ Resistivity, on the other hand, is the electrical resistance offered by a conductor to the flow of current through it. It is represented by “ρ “ and is pronounced “rho.’ The relation between conductivity and resistivity is:

σ =  1/ ρ  or ρ = 1/ σ

where;

σ is conductivity

ρ is resistivity

Main factors determining the resistivity of materials

As resistivity is the property of a material, it is dependent on certain factors. The main factors determining the resistivity of materials and their specific electrical resistance include:

• Temperature: Resistivity of a material depends on the temperature. It is common for metals to observe an increase with an associated increase in temperature.  Hence, metals have a positive temperature coefficient of resistance. The semiconductors and insulator’s resistance decrease with an increase in temperature and hence they have a negative temperature coefficient of resistance. Several metals observe zero resistivity at absolute zero conductivity. It is termed “superconductivity.” 

Temperature-dependent resistivity formula is given as:

t2=t1[1+(t2–t1)]

here,

ρt1: is the resistivity of the material at temperature t1o C

ρt2 is the resistivity of the material at temperature t2o C

α is the temperature coefficient of resistance of material at the temperature of t1o C 

• Alloying: When two or more solids are mixed to form a new solid, it is called alloying. Hence, it is done to get to the best mixture of certain properties of different metals in a single product. Due to this mixing, the atomic structure of a solid solution is irregular compared to the pure metals and hence the associated electrical resistivity of the solid solution or alloy is increased. This increase in electrical resistivity is directly proportional to the increase in alloy content. A small unit of impurity in the alloy can increase the metal’s resistivity. The impurity may have low resistivity that can significantly decrease the resistivity of pure conductors.

For example: If you want to increase the resistivity of copper, you can do it by adding silver which has the lowest resistivity in all metals. 

• Mechanical stressing: The development of the localised crystal strains on the crystal material structure is mechanical stressing. Hence, mechanical stressing causes a disturbance in the movement of the free electrons in the material. Hence, the resistivity of a material increases due to mechanical stressing. The opposite process to mechanical stressing is the annealing that removes the mechanical stress on the materials. It thus decreases the resistivity of the materials.

For example, hard-drawn copper has more resistivity compared to annealed copper. 

• Age hardening: It is also called “precipitation hardening.” In age hardening, the alloys develop the property to resist the permanent deformation by the external forces and hence increase their yield strength. It is achieved by creating solid impurities or precipitates to disturb the crystal structure of the metals. These impurities thus affect the passage of current and hence resistivity of the metal increases.
  
  
• Cold working: It increases the strength of metals and is called “strain hardening” or “work hardening.” It is used to increase the mechanical strength of the metal and disturbs the crystal structure of the metal. Hence, the metal resistivity increases due to cold working.

Conclusion

Hope all your queries about resistance are clear with our study material. The details about resistance, its applications in modern physics, and other concepts help understand the laying foundation of resistivity. The different factors affecting resistivity include temperature, etc.

While it is the natural tendency of any material to oppose the flow of current, different materials have different resistivities. This is due to the different sub-atomic configurations of the materials.