Question

A cylindrical conductor of radius $2\text{cm}$ is surrounded by another hollow cylindrical conductor of radius $20\text{cm}$. If the length of both the cylinders is $4.6\text{cm}$, then what is the capacitance of this system?
$(\ln 10=2.3)$

• A. $2.2\times {10}^{-12}\text{F}$
• B. $1.1\times {10}^{-11}\text{F}$
• C. $2.2\times {10}^{-11}\text{F}$
• D. $1.1\times {10}^{-12}\text{F}$

Answer 1

The correct option is D $1.1\times {10}^{-12}\text{F}$

Given:
$R_1=2\text{cm};R_2=20\text{cm};l=4.6\text{cm}$


For a cylindrical capacitor

$C=\frac{2\pi {ϵ}_{0}l}{\ln \left(\frac{R_2}{R_1}\right)}$

putting the data

$\Rightarrow C=\frac{1}{18\times {10}^9}\times \frac{4.6\times {10}^{-2}}{\ln \left(\frac{20}{2}\right)}$

$\Rightarrow C=1.1\times {10}^{-12}\text{F}$

Hence, option $\left(d\right)$ is correct.