Question

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

• A. $2.5\times {10}^6\text{mho/m}$
• B. $6.25\times {10}^5\text{mho/m}$
• C. $2.5\times {10}^9\text{mho/m}$
• D. $6.25\times {10}^{10}\text{mho/m}$

Answer 1

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

Given:
$A={10}^{-3}{\text{cm}}^2;V=2\text{V};I=0.25\text{A}$

From current- voltage relation, we know

$V=IR=I(\frac{l}{\sigma A})$

$\therefore \sigma =\frac{Il}{VA}=\frac{\left(0.25\right)\left(0.5\right)}{\left(2\right)\left({10}^{-7}\right)}$

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

Hence, option $\left(b\right)$ is correct.