Cylindrical Capacitor Formula

A cylindrical capacitor is a device that stores a significant amount of electric current in a small amount of area. It consists of a concentric hollow spherical cylinder encircling a hollow or solid cylindrical conductor. Electric motors, grain mills, electric juicers, and other electrical appliances all make use of cylindrical capacitors. A capacitor is designed to confine electric field lines to a confined area. As a result, even if the field is very strong, the potential difference between the two conductors of a capacitor is quite tiny. Although capacitors can be grouped in a variety of ways to achieve the necessary capacitance, the most common configurations are series and parallel. The formula for calculating cylindrical capacitance is presented in this article.

Cylindrical Capacitor

Capacitance per unit length is the capacitance for a cylindrical geometry.

Every capacitor’s potential difference is unique. There are a number of electrical circuits in which the capacitors must be arranged in the correct order to get the desired capacitance. Capacitors in series and capacitors in parallel are the two most prevalent configurations. Farad is the standard unit for capacitance (F). For the storage of electric charge, a cylindrical capacitor is commonly utilized.

Formula for Cylindrical Capacitor 

The Capacitance of a Cylindrical Capacitor can be calculated using the following formula:

C = 2πε₀ × (L / ln(b/a))

Where,

• C = Capacitance of Cylinder,
• ε₀ = Permittivity of free space,
• a = Inner radius of cylinder,
• b = Outer radius of cylinder,
• L = Length of cylinder.

Sample Questions

Question 1: Why are there so many cylinder-shaped capacitors?

Answer:

Two conducting plates are separated by an insulating gap in the general form of the capacitor. Metal foils, metalized polymer films, electrolytes, and other materials can all be used to create the insulating and conductive components. All of the items mentioned above can be built in a flat rectangular shape. Some capacitors aren’t spherical in shape. Stacking layers of insulating and conducting material alternately form them. Multilayer ceramic chip capacitors, for instance, are a good example.

Question 2: What are the components of a cylindrical capacitor? Give a few uses.

Answer:

A cylindrical capacitor consists of a cylindrical conductor encircled by a hollow spherical cylinder. Electric motors, grain mills, electric juicers, and other electrical instruments are among the most common uses for cylindrical capacitors.

Question 3: Calculate the capacitance of a cylindrical capacitor packed with paper and made up of cylinders with inner and outer radius of 2 cm and 5 cm, respectively.

Answer:

We substitute the permittivity, which equals 3.85 for paper, in the formula for the Capacitance of Cylindrical Capacitor, resulting in:

Given : ε₀ = 8.85 × 10^-12, L = 3.85, b = 5 cm, a = 2 cm.

Since,

C = 2πε₀ × (L/ln(b/a))

= 2 × 3.14 × 8.85 × 10^-12 × (3.85 / ln(5/2))

= 538.22 × 10^-12 F

Question 4: A cylindrical capacitor is made up of two rings with a 6 cm inner radius and a 12 cm outer radius. Calculate the capacitor’s capacitance based on its length of 16 cm.

Answer:

Given : a = 6 cm, b = 12 cm, L = 16 cm, ε₀ = 8.85 × 10^-12

Since,

C = 2πε₀ × (L/ln(b/a))

= 2 × 3.14 × 8.85 × 10^-12 × (16 × 10^-2 / ln(12/6))

= 2.954 × 10^-11 F

Question 5: A cylindrical capacitor with an 8 cm length is made up of two concentric rings with a 3 cm inner radius and a 6 cm outer radius. Calculate the capacitor’s capacitance.

Answer:

Given : a = 3 cm, b = 6 cm, L = 8 cm, ε₀ = 8.85 × 10^-12

Since,

C = 2πε₀ × (L/ln(b/a))

C = 2 × 3.14 × 8.85 × 10^-12 × (8 × 10^-2 / ln(6/3))

= 1.477 × 10^-11 F

Question 6: The length of a cylindrical capacitor is 9 cm. It is made up of two concentric rings with inner and outer radii of 2 cm and 7 cm, respectively. Calculate the capacitance of the capacitor.

Answer:

Given : a = 2 cm, b = 7 cm, L = 9 cm, ε₀ = 8.85 × 10^-12

Since,

C = 2πε₀ × (L/ln(b/a))

C = 2 × 3.14 × 8.85 × 10^-12 × (9 × 10^-2 / ln(7/2))

= 9.19488 × 10^-12 F