Temperature Dependence of Resistivity

Introduction

The electrical resistivity or the electrical resistance is an intrinsic property of a material. It is referred to as the measure of a material’s resistance to the electric current flow. It is denoted by ρ (rho). If the conductivity is higher, the resistivity of the material will be lower and vice-versa. It is often seen that the material’s resistivity is altered with the change in temperature. This study material on the temperature dependence of resistivity will discuss the temperature dependence of resistivity in length, as well as other related topics.

What is Resistance? 

Resistance can be defined as the measure of opposition, which is applied by an object, to the electric current flow. A resistor is an electronic constituent used in the circuit to offer a specific amount of resistance. The measuring unit of resistance is ohm (Ω). 

When the voltage is applied across a material, electrical current passes through it, which is directly proportional to the amount of current provided. It is denoted by V∝I. The constant proportionality is defined as the resistivity of the material resistance, which is denoted by V=RI. 

Thus, these resistances can be explained as the overall ratio of the voltage applied across the material to the current. 

What is the Unit of Resistance? 

The volt per ampere is the unit of resistance, which is denoted by Ohm (Ω). The name ohm has been given to remember a famous German physicist, Mr George Simon Ohm. Its unit can either be written in words or symbols. 

What is the Resistance of Various Materials? 

Materials can be divided into three major categories. These are as follows –  

Insulators

The electrical conductivity has a lower value for insulators. These are mainly used in electric circuits and systems to protect from current leakage. Here are several insulator materials. Example: porcelain, mica, paper, mineral oil, dry wood, nitrogen gas, etc.

Conductors

Conductors are objects that  allow flow of charge or flow of electric current. For example, let’s consider a metal rod.  When this rod is connected to the battery then electric charge flows through this metal. Conductors have very less resistivity. 

Semiconductors 

These are materials that contain a medium amount of conductivity and resistance. However, being a moderate conductor, these can be utilised in several areas of electronic devices. Some of the most sought semiconductors are germanium and silicon.

Temperature Dependence of Resistivity

According to the conductivity of the material, these are categorised into three major parts: insulators, conductors, and semiconductors. The conductors hold a low-temperature dependence of resistivity that ranges from 10-8Ω m to 10-6 Ω m. However, insulators contain a greater resistivity that can be more than 1018 times present in a material. 

The resistivity is indirectly dependent on the temperature, which means that if the temperature of a substance is decreased, the amount of reactivity will automatically increase. However, this does not apply to all types of materials. This is because not all materials possess the same amount of temperature dependence. 

However, the equation that describes the temperature dependence of resistivity is:

ρT= ρ0 [1 + a(T–T0)]

Where, 

ρT= resistivity at a temperature T

a= temperature coefficient of resistivity with a dimension of (Temperature)-1

ρ0 =resistivity at a reference temperature T0

Some materials, such as manganin, nichrome, and constantan, do not change their resistivity according to the temperature. Therefore, they fall under the category of wire bond standard resistors. Furthermore, the semiconductor materials have an indirect relationship with the temperature, where they will decrease when the temperature increases. 

Understanding the equation:

You already know that the ρ in resistivity is denoted with the formula: 

ρ= 1/σ = m/ne2ζ 

Where “n” denotes the number of free electrons in a material, ζ denotes the average time among collisions. These two are inversely proportional to ρ, which indicates resistivity. 

Further, with metals that do not change the ‘n’ with the temperature, the increase in the collision of electrons present in the metal can be noticed. However, in such a situation, the ζ will be reduced and further promotes the increment of the temperature when the ρ is increased. Nevertheless, for semiconductors and insulators, the n increases along with the increasing temperature, which further automatically decreases the resistivity ρ. 

Differences Between Resistance and Temperature

According to the universal rule, resistance in conductors increases if the temperature of the material increases. However, for insulators, the resistivity increases when the temperature starts to decrease. In some cases, semiconductors further decrease with the increment of the temperature. However, no simple mathematical relations are provided to identify the relationship among the temperature dependence of resistivity.

• Semiconductors – As the temperature increases, the conductivity of the element also increases. This is because, with the increment in the temperature, the outermost electrons attract energy, attracting the outer electrons leaving the shell of the atom. Thus, the increment in the conductivity is also noticed. This is also further performed for the insulator materials. 

• Conductors – For the conductors, the valence and the conduction band overlap with particles. Thus, this conduction band includes a high amount of electrons. In this way, it absorbs the energy and influences the electrons to go towards the conduction band from the valence band.  

Conclusion

With this, we come to an end of our today’s discussion about the temperature dependence of resistivity. Today, in this article, we covered multiple areas of temperature dependence of resistivity, including the definition of resistance, along with the unit of resistance. As discussed earlier, the volt per ampere is the unit of resistance. 

We also discussed conductors, insulators, and semiconductors and why they show such unique characteristics. We hope today’s topic has helped us understand the topic of temperature dependence of resistivity in detail.