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

The correct option is A $\frac{3}{\sqrt{\rho }}$

Volume $=$ Area $\times$ length

$3=Al$

$A=\frac{3}{l}$

Resistance $R=\rho \frac{l}{A}$

$3=\frac{\rho l}{\left(\frac{3}{l}\right)}=\frac{\rho l^2}{3}$

$l^2=\frac{9}{\rho }$

$\Rightarrow l=\frac{3}{\sqrt{\rho }}$