What is meant by resistance of a conductor? Name and define its SI unit. List the factors on which the resistance of a conductor depends. How is the resistance of a wire affected if: (i) its length is doubled, (ii) its radius is doubled?

Electrical resistance of a conductor is a measure of the opposition offered by it for flow of electric charge through it. Mathematically, resistance is given as:

Resistance R = Potential difference across the conductor V/Current I
SI unit of resistance is ohm Ω. Resistance of a conductor is said to be 1 Ω, if a potential difference of 1 volt is to be applied across its ends to maintain a flow of 1 ampere of current. The resistance R of a conductor is (a) directly proportional to its length L, (b) inversely proportional to its cross-section area A, and (c) depends on the nature of the material of the conductor. Thus,

R ∝ L/a or R = pl = pL/A,
where p is a constant depending upon the nature of the material of conductor and is known as its resistivity.
(i) The resistance of a wire is doubled if its length is double keeping other factors unchanged. It is because R ∝ L.
(ii) If radius of wire is doubled then its cross-section area (A =πr²) becomes 4 times of its original value. Since R ∝ 1/A hence the new resistance of wire becomes 1/4 th, of its original value.