Question

A spherical shell, made of material of electrical conductivity $\frac{{10}^9}{\pi }(\Omega -m{)}^{-1}$, has thickness $t=2mm$ and radius $r=10cm$, in an arrangement, its inside surface is kept at a lower potential than its outside surface.
The resistance offered by the shell is equal to -

• A. $5\pi \times {10}^{-12}\Omega$
• B. $2.5\times {10}^{-11}\Omega$
• C. $5\times {10}^{-12}\Omega$
• D. $5\times {10}^{-11}\Omega$

Answer 1

The correct option is D $5\times {10}^{-11}\Omega$

$R=\frac{\rho \cdot L}{A}=\frac{1}{\sigma }=\frac{L}{A}$

Here $L$ $=$thickness

$A=4\pi R^2$

$\therefore R=\frac{1}{\sigma }=\frac{1}{4\pi R^2}$

using values $R=\frac{\pi }{{10}^9}\times \frac{2\times {10}^{-3}}{4\pi {\left(10\times {10}^{-2}\right)}^2}$

$=R=5\times {10}^{11}\Omega$

Hence,

option $\left(D\right)$ is correct answer.