The specific resistance of a wire is $ρ$, its volume is $3 m^3$ and its resistance is 3 ohm, then its length will be
Answer & explanation
Correct answer: option 2
$ R = \frac{\rho l}{A}$
$ 3 = \frac{\rho l}{A}$
$\Rightarrow \frac{A}{l} = \frac{\rho}{3}$
$\Rightarrow V = Al = 3$
$\text{Multiplying these two equations }A^2 = \rho $
$ \Rightarrow A = \sqrt \rho $
$\Rightarrow l = \frac{3}{\sqrt \rho}$