Created By : awnish

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 10, 2023

The Spherical Capacitor Calculator is a free tool that determines the capacitance of the spherical capacitor by taking the required parameters. All you need to do is enter the inner radius and outer radius of the spherical capacitance in the input fields and press the calculate button to get the output in a fraction of seconds.

### How to Find Spherical Capacitance?

Get the simple steps to calculate the capacitance of the spherical capacitor easily in the following sections.

• Make a note of the capacitor inner radius and outer radius.
• Get the product of the relative permittivity, vaccum permittivity constants and 4π.
• Subtract the reciprocal of the outer radius from the reciprocal of the innwr radius of the sphere
• Divide the product by the subtracted value to obtain the capacitance.

### Capacitance of a Spherical Capacitor Equation

A capacitor is an electrical device that can store and release electric charge. These are used in many electronic devices to perform filtering, smoothing or bypassing the electrical signal. The amount of electric charge stored in a capacitor is known as capacitance.

Spherical capacitors can be connected either in series or parallel in a circuit. If the capacitor has three concentric spheres and space between them is filled with various dielectrics. When those capacitors are connected in series, then its equivalent capacitance reciprocal is the sum of the reciprocal capacitance of every individual capacitor.

If those capacitors are connected in parallel, then the total capacitance in the circuit is equal to the sum of the capacitance of the all-spherical capacitors.

The spherical capacitor with dielectric equation is as follows:

C = 4πε0εk/(1/a - 1/b)

Where,

C is the spherical capacitor capacitance

a is the inner radius of the spherical capacitor

b is the outer radius of the spherical capacitor

ε0 is the vacuum permittivity constant and its value is 8.85 × 10-12 F/m

εk is the relative permittivity and its value is 1

Example

Question: A spherical capacitor has an inner sphere radius of 32 cm and outer sphere radius of 35 cm. Determine the capacitance of the capacitor?

Solution:

Given that,

The radius of inner sphere a = 32 cm = 0.32

The radius of the outer sphere b = 35 cm = 0.35 m

Capacitance C = 4πε0εk/(1/a - 1/b)

C = (4π x 8.85 × 10-12 x 1)/(1/0.32 - 1/0.35)

= (111.21 x 10-12)/(0.03/0.112)

= (111.21 x 10-12)/0.267

= 415.184 x 10-12 F

Therefore, the capacitance of the spherical capacitor is 415.184 x 10-12 F.

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### FAQ's on Spherical Capacitor Calculator

1. What is the capacitance of a spherical capacitor?

The spherical capacitor capacitance is the amount of electrical charge stored in the capacitor. The formula of spherical capacitor with dielectric is C = 4πε0εk / (1/inner_radius - 1/outer_radius).

2. What is the capacitor?

A capacitor is an electrical device that has the ability to store electrical energy. It has two terminals and those are separated by a distance. The distance between the capacitor conductors may be filled by the vacuum or insulting material called the dielectric. The ability of a capacitor to store the electric change is the capacitance.

3. What is a spherical capacitor?

The spherical capacitor has two concentric conducting spherical shells of inner radius and outer radius. The shells have opposite charges and the electric field between shells is directed radially outward.

4. Why spherical capacitors are not used?

Practically, there is no electric device that uses a spherical capacitor. Because it is not possible to properly produce one economic usage if we think of concentric spheres one inside other.