Temperature Dependence Resistance

What is Resistance?

Resistance is the obstacle to the flow of electrons in the material. When a potential difference is applied across a conductor, it helps for the movement of the electrons while resistance opposes the movement of the electrons. A combination of those two factors is the rate at which charge flows between two terminals.

When a voltage is applied across a substance, an electrical current is produced. The voltage applied across the substance is, through it, directly proportional to the current.

V∝I

The proportionality constant is called the Resistivity of metals resistance.

V=RI

Hence resistance is defined as the ratio of the voltage applied through the substance to the current. Resistance is measured in ohms(Ω).


Unit of Resistance

From the concept of resistance, the unit of electrical resistance may be said to be volt per ampere. One unit of resistance is that resistance which allows one unit of current to flow through itself when one unit of potential difference is applied to it. The unit of resistance is volt per ampere is called ohm(Ω).


The Resistance of Different Materials

  1. Conductors: Those materials which offer very low resistance to the flow of electrons. Silver is a good electricity conductor but due to its high cost, it is not commonly used in electrical systems. Aluminum is a good conductor and is widely used as a conductor due to its low cost and abundance of availability.

  2. Semiconductors: Material that has a moderate value of resistance (not very high and not very low) at room temperature are known as semiconductors. There are several uses of semiconductors like for making electron devices. Silicon, germanium, are two materials mostly used for semiconductors. 

  3. Insulators: Those materials which offer very high resistance to the flow of electrons. These materials are very bad electricity conductors and mainly used in electric systems to prevent leakage current. Mica, porcelain, paper, dry wood, mineral oil, Nitrogen gas, air, etc are some good examples of insulators.


Resistance vs Temperature

The general rule says with resistance increases in conductors with increasing temperature and decreases with increasing temperature in insulators. In the case of semiconductors, typically, the resistance of the semiconductor decreases with the increasing temperature. But there is no simple mathematical relation to describe this relationship between resistance and temperature for different materials with graphs.

  1. For Conductor: The valence band and conduction band overlap with one another in the case of a conductor. So, a conductor's conduction band contains excess electrons. By absorbing the energy, more electrons will go from the valence band to the conduction band when you raise the temperature.

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  1. For Semiconductor: The conductivity of the semiconductor material increases with temperature increases. As temperature increases, outermost electrons acquire energy, and thus by acquiring energy, the outermost electrons leave the atom's shell.

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What is Resistivity?

Resistivity is basically the quantitative value of the resistance offered by any material. Although materials resist electrical current flow, some are better than others to conduct it. Resistivity is a figure that allows comparisons of how different materials allow or resist current flow.

The SI unit of resistivity is ohm⋅meter (Ω⋅m), commonly represented by the Greek letter ρ, rho.

The resistivity of a material can be defined in terms of the resistance (R), length (L), and area of the material (A). 

ρ=RA/L

From the equation, it can be seen that the resistance can be varied by adjusting a number of parameters.


Resistivity vs Temperature

The resistivity of materials depends on the temperature as ρt = ρ0 [1 + α (T – T0). This is the equation that shows the relationship between the resistivity and the temperature. 

ρt = ρ0 [1 + α (T – T0)

  • ρ0 is the resistivity at a standard temperature 

  • ρt is the resistivity at t0

  • T0  is the reference temperature

  • α is the temperature coefficient of the resistivity

Here is the relationship between the resistivity and the temperature with graphs.

  1. For Conductors: It is said that conductors have a positive co-temperature-efficient for metals or conductors. The positive value is α. For most metals, the resistivity increases linearly with temperature increases of around 500 K.

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  1. For Semiconductors: The resistivity of the semiconductor decreases with the increasing temperature.  It is said that they have a negative temperature coefficient. The temperature coefficient of resistivity, α, is therefore negative.

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  1. Insulators: For insulators, as the temperature increases, the material conductivity is increased. When the material's conductivity increases, we know that the resistivity decreases, and the current flow increases thereby. And certain insulators convert to conductors at high temperatures at room temperature. They have a negative temperature coefficient. 


Fun Facts

  • The main reason for the resistor as an electrical component is to resist electricity. 

  • The value of a resistor is easily measured by ohmmeter or multimeter.   

FAQ (Frequently Asked Questions)

1. What is The Difference Between The Resistivity And The Resistance?

The resistance is the material property that obstructs the current flow, while the resistivity gives the resistance of the material that has a fixed dimension. The resistance is the ratio of the conductor's length and cross-section area while the material's resistivity is the ratio of the resistance component and area to the conductor's length. Resistance is shown by R and resistivity is shown by ρ. The resistance of the material depends upon the length, cross-section, and the area whereas the resistivity depends on the material's temperature and nature.

2. What is The Cause Of Resistance?

A conductor's resistance implies the opposition that the conductor is offering to the charge flow through it. When a potential difference is applied across a conductor, the two ends of an electric field are set. The metal has a large number of electrons and an equal number of positive ions that do not move while free movement of electrons. The free electrons get accelerated because of this. As the electrons move, the ions and atoms clash and their motion is therefore opposed. This opposition provided by the ions and atoms is called conductor resistance.