question_answer

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?

Answer:

The property of a conductor which tends to restrict the flow of current through the conductor is called resistance.

SI unit of resistance is ohm. When a potential difference of 1V across a wire gives rise to 1A current through the wire, then the resistance is   said to be 1 ohm \[(1\,\Omega )\].

The resistance of conductor depends on length, thickness, nature of material and temperature of conductor.

(i) If the length is doubled, then R is doubled because the resistance of a conductor is directly proportional to length.

(ii) Resistance of a conductor is inversely proportional to the square of its diameter or area of cross-section. So, if the radius of conductor is doubled, its resistance becomes one-fourth.

\[R\propto \frac{1}{A}\]

and       \[A=\pi {{r}^{2}}\]

If          \[r'=2r,\] then

\[A'=\pi r{{'}^{2}}=\pi {{(2r)}^{2}}=4\pi {{r}^{2}}=4A\]

If  \[A=4A,\] then

\[R'=\rho \frac{L'}{A'}=\rho \frac{L}{4A}\mathrm{ }=\frac{1}{4}\left( \rho \frac{L}{A} \right)\]

\[=\frac{1}{4}R\]

Therefore, if radius is doubled, the resistance becomes one fourth.