Question

The capacitance of a cylindrical capacitor can be increased by:

• A. increasing the radius of the outer cylindrical shell and decreasing the length
• B. only by decreasing the length
• C. decreasing the radius of the inner cylinder and increasing the radius of the outer cylindrical shell
• D. increasing both the radius of the inner cylinder and the length

Answer 1

The correct option is D increasing both the radius of the inner cylinder and the length

The capacitance of a cylindrical capacitor of length $l$, having inner radius $a$ and outer radius $b$ is given by:

$C=\frac{2\pi {\epsilon }_{0}l}{{\log }_e\left(b/a\right)}$

From above equation:

$C\propto l$

It is clear that with increase in length l, capacitance C will increase.

And $C\propto \frac{1}{{\log }_e\left(b/a\right)}$

if we increase $a$, value of ${\log }_e\left(b/a\right)$ will decrease and it results in an increase in capacitance C.