Question

A wire of length 1 m and of radius 0.1 mm has a resistance of $100\Omega$.The resistivity of the material..............

• A. $0.0214\Omega -m$
• B. $3.14\times {10}^{-8}\Omega -m$
• C. $3.14\times {10}^{-6}\Omega -m$
• D. $0.00214\Omega -m$

Answer 1

Answer: (C)

$3.14\times {10}^{-6}\Omega -m$

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

$⟹R=\rho \frac{L}{\pi r^2}$

$⟹\rho =\frac{R\pi r^2}{L}$

$⟹\rho =\frac{100\times 3.14\times ({10}^{-4}{)}^2}{1}$

$⟹\rho =3.14\times {10}^{-6}\Omega -m$