Here, we will explore the concept of resistivity in detail, including its definition and the resistivity of various materials such as conductors, semiconductors, and insulators, and also read about the temperature dependence of resistivity. All this content is related to the NCERT Chapter 3 Physics curriculum for class 12. This article is also useful for students preparing for NEET, CBSE, NCERT, and other educational boards.
Resistivity
The resistance (R) of the conductor is directly proportional to the length.
`R \prop l`
The resistance (R) of the conductor is inversely proportional to the cross-section area (A) of the conductor.
`R \prop \frac{1}{A}`
From eq. 1 and eq. 2
`R \prop \frac{l}{A}`
`R = \rho \frac{l}{A}`
Where `\rho` is the proportionality constant and is known as resistivity. It depends on the material of the conductor but not on its dimensions.
According to Ohm's law
`V = I \times R`
`V = I \times \rho \frac{l}{A}`
`V = J \times \rho \times l`
`E \times l = J \times \rho \times l`
`E = J \times \rho `
`E = \rho \times J `
This equation often states Ohm's law.
Here, `\frac{1}{\rho} = \sigma` where `\sigma` is called the conductivity.
Where,
I = Current
` J = \frac{I}{A}` = current density (current per unit area)
The SI units of the current density are `\frac{A}{m^2}`
`\rho` = resistivity of the conductor
E = Magnitude of uniform electric field
`l` = Length of conductor
V = Potential difference across ends of the conductor
Resistivity of Various Materials
We classify materials into various types based on their electrical properties, including conductors, semiconductors, and insulators.
Conductors
Metals have low resistiveities in the range of `10^{-8}` to `10^{-6} \Omega m`
Conductors allow the easy flow of electric current due to their low resistance.
Conductors have low resistivity and high conductivity.
Examples of conductors are metals such as copper, aluminum, and silver.
Insulators
Insulators have very high resistivity `10^{18}` greater than metals or more.
Insulators have low conductivity.
Insulators are used in electrical and electronic systems to isolate conductive components and protect against short circuits.
Examples of insulators are ceramic, rubber, and plastics.
Semiconductors
Intermediate resistivities between conductors and insulators.
Current carriers in semiconductors are holes and electrons.
Examples of semiconductors are silicon (Si) and germanium (Ge).
Temperature Dependence of Resistivity
Conductor
The resistivity of a metallic conductor is approximately given by,
`\rho_T = \rho_0 [1 + \alpha (T - T_0)]` ....(1)
Where,
`\rho_T =` Resistivity at a temperature T
`\rho_0 =` Resistivity at a temperature `T_0`
`\alpha =` Temperature co-efficient
For metal `\alpha` is positive.
Equation (1) can be used approximate over a limited range of T around any reference temperature `T_0`, where the graph can be approximated as a straight line.
 |
| Resistivity and Temperature Graph |
Nicrome is an alloy of nickel, iron, and chromium that exhibits a very weak dependence on resistivity with temperature. Some other materials are manganin and constantan which have the same properties. Materials like nichrome, manganin, and constantan are used in wire-bound because their resistance would change very little with temperatures.
We know that the resistivity of a conductor is
`\rho = \frac {m}{n e^2 \tau}` and
`R = \frac{\rho l}{A}`
In the case of a conductor, on heating, an electron gets excited and the range of collision increases and relaxation time decreases, so resistivity increases.
Resistivity increases with temperature.
The graph between resistivity and temperature for conductor
 |
| Resistivity and Temperature Graph |
Semi-Conductor
In the case of a semi-conductor, the heating current carriers (holes and electrons) increases and hence resistivity decreases.
Resistivity increases with an increase in temperature.
The graph between resistivity and temperature for conductor
 |
| Resistivity and Temperature Graph |
What is the effect of temperature on resistance?
Effect of Temperature on Resistance
With the increase in temperature, the kinetic energy of free electrons, in the conductor get increased i.e. collision between the electrons also increases, due to which relaxation time is reduced then according to `R = \frac{m l}{n A e^2 \tau}`, resistance increases.
No comments:
Post a Comment