A potential difference 'V' is applied across a conducting wire of diameter 'd' and length 'L'. When the diameter is doubled keeping the length same, the Resistance:

The correct answer is option 1) i.e. becomes (1/4)th of the initial value

CONCEPT:

Resistance: The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.

It is denoted by R and the SI unit is the ohm (Ω).

The resistance is given by:

\(R=\frac{\rho l}{A}\)

EXPLANATION:

\(R=\frac{\rho l}{A}\)

Since \(A = πr^2 =\pi(\frac{d}{2})^2\)

∴ The resistance will therefore be inversely proportional to the square of the diameter.

So, if the diameter is doubled, the resistance will be reduced to (1/4)th of the initial value.