Question

The specific resistance of a wire is $ \rho $ , its volume is $3m^3$ and its resistance is $ 3\Omega $ , then its length will be

• A. $ \frac{3}{\sqrt{\rho }} $
• B. $ \frac{\sqrt{3}}{\rho } $
• C. $ \frac{5}{\sqrt{\rho }} $
• D. $ \frac{\sqrt{5}}{\rho } $

Answer 1

Answer: (A)

Volume $=$ Area $\times$ length
$3= Al$
$A =\frac{3}{1}$
Resistance $R =\rho \frac{1}{ A }$
$3=\frac{\rho l}{\left(\frac{3}{1}\right)}=\frac{\rho l^{2}}{3}$
$1^{2}=\frac{9}{\rho}$
$\Rightarrow 1=\frac{3}{\sqrt{\rho}}$