Question

A nichrome wire $50cm$ long and $1m{m}^2$ cross-section carries a current of $4A$ when connected to a $2V$ battery. The resistivity of nichrome wire in ohm-meter is

• A. $1\times {10}^{-6}$
• B. $4\times {10}^{-7}$
• C. $3\times {10}^{-7}$
• D. $2\times {10}^{-7}$

Answer 1

The correct option is A $1\times {10}^{-6}$

$V=IR$

$R=\frac{2}{4}=\frac{1}{2}$

$\Rightarrow R=\frac{\rho L}{A}$

$\Rightarrow \frac{1}{2}=\frac{\rho \times \frac{1}{2}}{1\times {10}^{-6}}$

$\Rightarrow \rho ={10}^{-6}\Omega m$