Question

The resistance of one ohm is very approximately equal to that of a column of mercury $1.06m$ long and of uniform cross-section of one hundredth of $1c{m}^2$. Find the resistivity of mercury.

• A. $6.4\times {10}^{-7}\Omega m$
• B. $7.4\times {10}^{-7}\Omega m$
• C. $9.4\times {10}^{-7}\Omega m$
• D. $2.4\times {10}^{-7}\Omega m$

Answer 1

Answer: (C)

$9.4\times {10}^{-7}\Omega m$

Resistance, $\left(R\right)=$ $\rho \frac{l}{A}$ where $\rho$ is resistivity, $l$ is the length and $A$ is the cross sectional area.
Now $1$ ohm is equal to very approximately that of a column of mercury $1.06m$ long and of uniform cross-section of one hundredth of $1c{m}^2$=${10}^{-6}{m}^2$Putting the values of $R,l$ and $A$
$\rho =\frac{{10}^{-6}}{1.06}=9.43\times {10}^{-7}$