# Cylindrical Capacitor Formula

## What is a Cylindrical Capacitor?

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.

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).

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?

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

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1. Explain If a Capacitor Can be Charged Indefinitely?

Answer: If we are gradually charging it (it means that the provided voltage is within its rated voltage), it will keep on assimilating the charge from the flow of current until it creates a potential equal and an opposite to the supply voltage. Then, because of the capacitor's potential, the current flow can be stopped, and the capacitor charge will remain constant.

If we supply a larger voltage to the capacitor, the material present inside the capacitor undergoes a "breakdown," causing it to conduct between the terminals and hence causing the current to flow freely through it.

2. Explain Why Many Capacitor Types are Available in Cylindrical Shapes?

Answer: The basic form of the capacitor is given as two conductive plates, which are separated by an insulating gap. There are multiple ways of manufacturing the insulating and conductive components, with metal foils, metalized polymer films, electrolytes, and more. But, all of these can be made in a flat rectangular form.

A few types of capacitors are not cylindrical and tend to be made by the stacking layers that alternate between insulating and conducting material — for example, Multilayer ceramic chip capacitors.

3. Explain the Cause of the Capacitor Explosion?

Answer: The basic reason to explode a capacitor is overvoltage. The capacitor consists of two conducting parts, including the insulation material (which is di-electric) between them. That insulation has di-electric strength up to some certain limit. If any high voltage greater than rated can be applied across the capacitor, its di-electric strength will suddenly break down, and eventually, the capacitor will explode.

4. Why are the Motors Cylindrical in Shape?

Answer: The round shape is the most efficient for heat dissipation, and it uses the least amount of metal in the manufacturing process. The rotor inside has to be round to contain the smallest distance between it and the magnetic field of the stator winding for maximum efficiency. This specific stator magnetic coupling rotates the armature.

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