Question

The potential difference across a straight wire of ${10}^{-3}{\text{cm}}^2$ cross-sectional area and $50\text{cm}$ length, is $2\text{V}$, when a current of $0.25\text{A}$ flows in the wire. Calculate the conductivity of the metal.

• A. $6.25\times {10}^7\text{mho/m}$
• B. $6.25\times {10}^5\text{mho/m}$
• C. $6.25\times {10}^6\text{mho/m}$
• D. $6.25\times {10}^8\text{mho/m}$

Answer 1

The correct option is B $6.25\times {10}^5\text{mho/m}$

The magnitude of electric field in the wire is given as,

$E=\frac{V}{d}$

$\Rightarrow E=\frac{2}{0.5}=4\text{V/m}$

Current density in wire is given as,

$J=\frac{I}{A}$

$\Rightarrow J=\frac{0.25}{{10}^{-7}}=2.5\times {10}^6{\text{A/m}}^2$

The conductivity of the material is given as,

$\sigma =\frac{J}{E}$

$\Rightarrow \sigma =\frac{2.5\times {10}^6}{4}=6.25\times {10}^5\text{mho/m}$

Hence, option $\left(B\right)$ is the correct answer.