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.
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