Question

The specific resistance of wire of length 1 m, area .of cross-section $ 0.5\,{{m}^{2}} $ is $ 25\,\mu \Omega \,m $ . The resistance of the wire will be:

• A. $ 5\times {{10}^{-5}}\,\Omega $
• B. $ 3\times {{10}^{-6}}\,\Omega $
• C. $ 46\times {{10}^{6}}\,\Omega $
• D. $ 2\times {{10}^{6}}\,\Omega $

Answer 1

Answer: (A)

Resistance $R$ of a given conductor, at a constant temperature, is directly proportional to its length and inversely proportional to its area of cross-section $A$.
i.e., $R \propto \frac{l}{A}$ or $R=\rho \frac{l}{A}$
where $\rho$ is called the specific resistance of the material.
Given, $\rho=25 \times 10^{-6} \Omega m, l=1 m, A=0.5 m ^{2}$
$R=\frac{25 \times 10^{-6} \times 1}{0.5}$
$=50 \times 10^{-6}$
$=5 \times 10^{-5} \Omega$