The capacitor can be used to store large amounts of electric current in a smaller space. A hollow or solid cylindrical conductor is enclosed by a concentric hollow spherical cylinder in the cylindrical capacitor. Capacitors can be used widely in flour mills, electric motors, electric juicers and also in other electrical instruments.
About Cylindrical Capacitor
The potential difference between every capacitor differs. There are several electrical circuits where the capacitors are to be grouped accordingly to result in the desired capacitance. There exist two common modes, which are capacitors in series and capacitors in parallel. The unit of capacitance is given by Farad (F).
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Cylindrical capacitor is often used for the storage of electric charge. It is a type of capacitor, which possesses the shape of a cylinder having an inner radius as ‘a’ and the outer radius as ‘b.’
The Formula for the Capacitance of Cylindrical Capacitor Formula is Given as:
C = 2πε0[frac{L}{ln(frac{b}{a})}]
This is the cylindrical capacitance formula or the cylindrical capacitor formula derivation. It is also called a cylindrical capacitor equation.
Where,
C is the capacitance of the cylinder, a is the inner radius of the cylinder, L is the length of the cylinder, and b is the outer radius of the cylinder
Solved Example
Example: A Cylindrical capacitor, which is having a length of 8 cm is made of two concentric rings including an inner radius of 3 cm and the outer radius of 6 cm. Then, find the capacitance of the capacitor?
Answer: Given that,
Inner radius a = 3 cm,
Length L = 8 cm, and
Outer radius b = 6 cm.
The Formula for the Cylindrical Capacitor is Given as:
C = 2πε0[frac{L}{ln(frac{b}{a})}]
C = (2)(3.14)(8.85x10-12)(8x10-2)/ln[(frac{6}{3})]
C = 444.62x10-14/0.301
C = 1.477x10-11F