question_answer

The resistance of a wire of 0.01 cm radius is \[10\,\Omega \]. If the resistivity of the material of the wire is \[50\times {{10}^{-8}}\,ohm\] metre, find the length of the wire.

Answer:

Given: Resistance of a wire, \[R=10\,\Omega \]

Radius, \[r=0.01\,cm=0.01\times {{10}^{-2}}m\]

Resistivity, \[\rho =50\times {{10}^{-8}}\,\Omega m\]

Area of cross-section A,

\[=\pi {{r}^{2}}=3.14\times {{(0.01\,\times {{10}^{-2}})}^{2}}\]

\[=3.14\times 0.01\times 0.01\times {{10}^{-4}}\]

\[=3.14\times {{10}^{8}}\,{{m}^{2}}\]

We know,

\[R=\rho \frac{l}{A}\]

or         \[l=\frac{R\mathrm{ }\times \mathrm{ }A}{\rho }=\frac{10\times 3.14\times \mathrm{ }{{10}^{-8}}}{50\mathrm{ }\times \mathrm{ }{{10}^{-8}}}=0.628m\]