Temperature Dependence 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 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 per 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: Materials that have 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 are 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 that 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.

• 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.

• 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.

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 C 

• 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.

2. 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.

3. 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 an ohmmeter or multimeter.  

The study of electricity and power in physics is the most interesting chapter if the related concepts and formulas are understood well. The Vedantu website explains the flow of current and its resistance power very beautifully and naturally so that the students can understand them easily. The experts have curated special videos on how the entire thing works and have explained the concepts so very well. Students can just refer to these materials available online and prepare well for their exams.

Resistance is defined as a measure of the opposition to the flow of current induced by voltage in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω). A force, such as friction, operates opposite the direction of motion of a body and tends to prevent or slow down the body's motion. A simple example of resistance would be a child fighting against her kidnapper or the wind against the wings of a plane.

If you know the total current flowing and the voltage across the whole circuit present in any particular area, you can find the total resistance using 

Ohm's Law: R = V / I.

For example, a parallel circuit has a voltage of 9 volts and a total current of 3 amps. The total resistance RT = 9 volts / 3 amps = 3 Ω.

Resistance vs Temperature

As the temperature rises, the number of phonons increases, and with it the likelihood that the electrons and phonons will collide. Thus when the temperature goes up, resistance goes up. For some materials, resistivity is a linear function of temperature. The resistivity of a conductor increases with temperature.