Question

If a wire has resistivity $\rho$, volume $3m^3$ and resistance $3\Omega$ , then its length would be:

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

Answer 1

The correct option is B $3\times \sqrt{\frac{1}{\rho }}$

We know that,
$Volume=Area\times length$
Given :
Volume = $3m^3$
Resistance= $3\Omega$
$\Rightarrow Area=\frac{3}{length}=\frac{3}{l}$
Now, $R=\rho \frac{l}{A}$
where A is the area and l is the length
$\Rightarrow 3=\frac{\rho \times l}{3/l}=\frac{\rho l^2}{3}\Rightarrow l^2=\frac{9}{\rho }$
$\Rightarrow l=\frac{3}{\sqrt{\rho }}$.