Calculation of Capacitance

Calculation of capacitance is a very simple formula. Before entering the calculation, it is important to understand the concept of calculation of capacitance. The calculation of capacitance means determining the capacitance by charge stored in the capacitor and its electric potential. Also, it is measured in farads. 

How is the Calculation of Capacitance Performed?

The basic formula used for the calculation of capacitance is C=QV. 

What is a Capacitor?

A capacitor has the capability of storing energy in electric charge form. It is an electrical device with two electrical conductors separated by a space filled by a vacuum or insulating material, called a dielectric. 

An electronic device that stores charge and releases it when it gets full is called a capacitor. Applications of capacitors are computers, televisions, etc. Every electronic device that has been used as a capacitor has this implemented in it. Capacitors can store a small to a high amount of energy.

What is Capacitance?

The capability of a capacitor to store charge is widely known as capacitance. In other words, if there is a positive charge that moves into a region, then the other positive charges find it difficult to move in the same region, because the similar charges have the habit of repelling each other. Higher energy is required to move the additional positive charges present in the region, and an increase in voltage reflects this. The voltage will ultimately increase if there is a moving charge present in the region. 

How Does a Capacitor Work?

For example, consider the parallel plate capacitor, which has two parallel plates separated by an insulating material called a dielectric. Once the DC voltage has been connected, plate 1 and plate 2 will be connected to positive and negative ends, respectively. Plate 1 will become positive when the battery is connected since plate 2 is negative – the current flows across the capacitor from positive to negative plates when the condition is steady. The current does not flow across the capacitor since the insulating material is placed between the plates.

After a certain amount of time, according to the voltage supplied, the capacitor will hold a large number of charges. This phase of time is called a capacitor’s charging time.

The capacitor acts as a source of electrical energy once the battery is removed, and the parallel plates will hold a positive and negative charge for some time.

If the loads have been connected in plates, then the current flows from plate 1 and plate 2 to the load until both the plates deplete all the charges. Letting out all the charges from plates is called capacitor discharging time.

How do you Determine the Value of Capacitance?

The plates have charges such as q1 and q2. Plate 1 will have a positive charge, whereas plate 2 will have a negative charge. The formula below helps calculate capacitance by using the electric charge and potential created:

Q∝V

Q=CV

C=Q/V 

The change in electric charge concerning the electric potential is called capacitance. The importance of calculation of capacitance is that it measures the charge stored in a capacitor and the electric potential to act on it.

Depending on the usage of any capacitor, the capacitance can be determined as constant or variable. Capacitance depends on the insulating material and the size of the capacitor.

The Capacitance of a Parallel Plate Capacitor

Let us consider a parallel plate capacitor that has two plates. The surface area is “A”, and the distance between them is “d”. Dielectric medium is the air filled between the plates. Voltage “V” was applied to both the plates to store the charge “Q”.

The force created between the charge raises the values of the charge and reduces the distance between the plates. The charge stored will be huge depending upon the larger distance created between the plates. If the plates are closer, the attraction of the opposite charges will be more. 

• Capacitance is greater for large surface areas. 
• Capacitance is greater for the smaller distance created between the plates.

Below is the density of the plates:

σ=Q/A

For a small distance, the electric field created between the plates will be uniform, and the magnitude will be:

E=σ/ϵ0

If the electric field created between the plates is uniform, the potential difference will be: 

v=Ed=σd/ϵ0=Qd/ϵ0A

Using the value of V in the capacitance: 

C=Q/V=Q/(Qd/ϵ0A)=ϵ0A/d

The Capacitance of a Parallel Plate Capacitor, C=ϵ0A/d

Example

Estimate the capacitance of a parallel plate capacitor which is empty and has two metal plates whose area is 1.00 m2; distance is 1.00 mm.

Solution

Capacitance formula:

C=ϵ0A/d

Applying the given values:

C = (8.85×10−12F/m) 1m2/(1 × 10−3m)

   = 8.85×10−9F = 8.85nF

Capacitance Calculation of a Spherical Capacitor

Spherical capacitors usually have two concentric conducting spherical shells of radii R1 and R2. It has both equal and opposite charges +Q and –Q. The electric field created between the shells is directed radially outward. The magnitude of the field is determined by substituting Gauss’s law over a surface of radius r.

The enclosed charge is +Q 

∮SEdA=E(4πr2)=Q/ϵ0

The electric field:

E=1/(4πϵ0)  x Q/r2

Integrating E between the shells, 

V=R1R2Edl = Q/(4πϵ0) x (1/R1−1/R2)

Two conductors’ potential difference: 

VB−VA=-ABEdl

The potential difference b/w the plates: 

V= −(V2−V1) =V1−V2

Applying the value of V in capacitance:

C=Q/V=4πϵ0 x (R1R2)/(R2−R1)

The capacitance of a spherical capacitor C=4πϵ0(R1R2)/(R2−R1).

Conclusion

The calculation of capacitance can be estimated by the amount of increase in voltage completely depending upon the stored charge. Calculation of capacitance measures the capacitor’s capability to store energy in the form of charge. It can be used in various applications. Each application has various advantages and characteristics related to capacitance.