Question

State and explain the laws of resistance.

Answer 1

The following are the main laws of resistance:
(i) Resistance of a conductor is directly proportional to its length, provided temperature and other physical conditions remain unchanged.
It means that R ∝ l i.e., if the length increases, the resistance also increases and if length decreases, its resistance also decreases.
(ii) Resistance of a conductor is inversely proportional to its area of cross section, other conditions remaining the same.

If A is the area of cross section, then:

R α `1/"A"`

or    R α `1/(pi"r"^2)`

where r is the radius of the wire

Keeping the length same, if the radius of the wire is doubled then:

R α `1/(2"r")^2` α `1/"4r"^2`

or R α `1/4 . 1/(pi"r"^2)`, or R becomes one fourth.

Similarly if r is made half, then:

R α `1/("r"/2)^2`

α `4/"r"^2 α  4 (1/"r"^2)`, orR becomes 4 times

This shows that R is α `1/"A"`

(iii) R depends on the nature of the material of the conductor. It means, if we take equal lengths of wires of copper, aluminium and iron and all of the same cross-sectional area, their resistance are different from each other since they are of different materials.