Resistance and resistivity

Resistance: 

The flow of electrons is not so free inside a metallic conductor. Just like  flow of water in a river is opposed by the presence of big rocks in its way, the flow of electrons is similarly opposed by stationary atoms and repulsion by other electrons.

The typical speed of an electron moving inside a metal is of the order of \(10^6\) m/s. It however collides million times in a second and it barely moves 1mm in a unit second.

This property of a conductor to resist the flow of charge through it is called resistance.

SI unit :

Its SI unit is ohm, represented by the Greek letter Ω.

Definition of 1Ω: 

If the potential difference across the two ends of a conductor is 1 V and the current through it is 1 A, then the resistance R, of the conductor is 1 Ω. That is,
\[R=\frac{V}{I}\]
\[1\;ohm=\frac{1\;volt}{1\;ampere}\]
\[\textrm{or }1\;Ω=\frac{1\;V}{1\;A}\]

Relation between current and resistance: 

According to Ohm’s Law, 

\[I=\frac{V}{R}\]

the current through a resistor is inversely proportional to its resistance. If the resistance is doubled the current gets halved.

Since I is inversely proportional to the resistance of the circuit for a given V, we use this concept in controlling the amount of current in a domestic circuit by using a variable resistors.

Application of varying resistance: 

In many cases it is necessary to increase or decrease the current in an electric circuit like in case of an electric fan regulator and in electric iron for changing the amount of heat produced. The device used to control current without changing the voltage is called variable resistance.

 Symbol of variable Resistance:

Symbol of Rheostat ( a variable resistor):

Resistance of different material is different: 

The motion of electrons in an electric circuit constitutes an electric current. The electrons, however, are not completely free to move within a conductor. They are restrained by the attraction of the atoms among which they move. Thus, motion of electrons through a conductor is retarded by its resistance.

• A component of a given size that offers a low resistance is a good conductor.
• A conductor having some appreciable resistance is called a resistor.
• A component of identical size that offers a higher resistance is a poor conductor.
• An insulator of the same size offers even higher resistance.

Factors on which the resistance of a conductor depends: 

Resistance of the conductor is 

(i) Directly proportional to its length, 

(ii) Inversely proportional to its area of cross-section, and 

(iii) On the nature of its material. 

That is, 

\[R∝l ----(1)\]

\[R∝\frac{1}{A}----(2)\]

Combining (1) and (2)

\[R∝\frac{l}{A}\]

Or

\[R∝ρ\frac{l}{A}\]

Where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor. 

Resistivity of a given material is independent of the dimension (i.e. length and area of cross-section) of given material and it depends only on nature of material and temperature. 

SI unit of resistivity: 

The SI unit of resistivity is Ω m. It is a characteristic property of the material.

Remarks: 

(1) The metals and alloys have very low resistivity in the range of 

\[10^{-8}ᘯ\;m\quad\textrm{to}\quad 10^{-6}ᘯ\;m\]

They are good conductors of electricity.

(2) Insulators like rubber and glass have resistivity of the order of

\[10^{12}ᘯ\;m\quad\textrm{to}\quad 10^{17}ᘯ\;m\]

(3) Both the resistance and resistivity of a material vary with temperature.

(4) Resistivity of a material does not change on changing the length and area of cross-section of the conductor.

(5) Resistivity of an alloy is generally higher than that of its constituent metals.

(6) Alloys are used in electrical heating devices, like electric iron, toasters etc because they do not oxidise (burn) readily at high temperatures.

(7) Tungsten is used almost exclusively for filaments of electric bulbs, because it does not melt at higher temperature, have high resistivity and can be easily drawn in to thin wires. 

(8) Copper and aluminium are generally used for electrical transmission lines because of their low resistivity they behave as a good conductor of electricity.

NOW CHECK YOUR PROGRESS!!!

1. A wire of given material having length l and area of cross-section A has a resistance of 4 Ω. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A?

2. A wire of resistance 20 Ω is stretched to double its length. What will be its new (i) resistivity (ii) resistance?

3. On what factors does the resistance of a conductor depend?

4. Define the SI unit of resistance.

5. Why is the tungsten used almost exclusively for filament of electric lamps?

6. Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?

7. How does the resistance of a wire vary with its area of cross-section?

8. Why copper and aluminium wires are usually employed for electricity transmission?

9. Give two examples of materials which are (i) good conductor (ii) resistor (iii) insulator (iv) poor conductor.

10. Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?

11. Why do electricians wear rubber hand-gloves while working with electricity?

12. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?

13. Name the device used to change resistance in a circuit to regulate current without changing the voltage source.

14. What is nichrome? State its one property and one use.

15. On what factor does the resistivity of a material depends?