Question

The temperature coefficient resistivity of a material is $0.0004/K$. When the temperature of the material is increased by ${50}^{o}C$, its resistivity increases by $2\times {10}^{-8}ohm-meter$.The initial resistivity of the material of the resistance

• A. $50\times {10}^{-8}$
• B. $90\times {10}^{-8}$
• C. $100\times {10}^{-8}$
• D. $200\times {10}^{-8}$

Answer 1

The correct option is C $100\times {10}^{-8}$

$(\rho -{\rho }_0)={\rho }_0\propto \Delta T$ (using standard result)
$\Rightarrow 2\times {10}^{-8}={\rho }_0\times 4\times {10}^{-4}\times 50$
$\Rightarrow 2\times {10}^{-8}={\rho }_0\times 2\times {10}^{-2}$
$\Rightarrow {\rho }_0=100\times {10}^{-8}ohm-meter$