Question

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

• A. $\frac{\sqrt{1}}{\rho }$
• B. $\frac{3}{\sqrt{\rho }}$
• C. $\frac{1}{\rho }\sqrt{3}$
• D. $\rho \sqrt{\frac{1}{3}}$

Answer 1

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

The resistance of the wire is

$R=\frac{\rho L}{A}$ .............................(1)

where, variables have their usual meanings.

Now, the volume is

$V=AL$

$AL=3m^3$.....................(given)

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

from (1)

$R=\frac{\rho L}{\frac{3}{L}}$

$3=\frac{\rho L^2}{3}$ .......................(since, $R=3\Omega$)

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

$L=\frac{3}{\sqrt{\rho }}$