Dimensional Formula of Capacitance

Capacitors are found in nearly every electronic gadget in our environment. There are many capacitors of all sizes, from a fan to a chip. The capacitor’s primary function is to store energy in theory. Energy storage, voltage spike prevention, and signal processing are popular applications. Ewald Georg von Kleist, a German physicist, invented it in 1745. A capacitor is nothing more than two conductors separated by an insulator. They can hold a charge that provides them with many of their characteristics. Let us take a closer look in detail. 

Capacitance is called the limitation of the storage capacity of the electric charge. Every capacitor has its capacitance. There are two metallic plate areas A in a typical parallel plate capacitor, separated by the distance D.

Capacitance formula

C = k ε0A/d

Here, ε0 is the permissive space. (8.854 × 10-12 F/m)

k represents the similar permittivity of dielectric material

d is the separation between the plates.

A is the area of plates.

Dimensional Formula of Capacitance

Capacitance = Charge × Voltage

C  = QV

We know that charge = Current × Time

And voltage = Electric field × Distance

Electric field = Force x Charge

Dimension formula of force = [M1 L1 T -2]

Dimension formula of Charge = [I1 T1]

Dimension formula of Electric field = [M1 L1 T-2] [I1 T1]-1 = [M1 L1 T-3 I-1]

Dimension formula of Voltage = [M1 L1 T-3 I-1][L] = [M1 L2 T-3 I-1]

Dimension formula of Capacitance = Charge × Voltage = [I1 T1] [M1 L2 T-3 I-1]-1

Therefore, now we will get Dimensional Formula of Capacitance = [M-1 L-2 T4 I2]

Concept Of Capacitor And Capacitance: 

The capacitor is known as an electric condenser. It is a two-terminal electronic component. It has the capacity or ability to store energy in the electric charge form. It is usually designed to enhance the effect of capacitance. This is the relation between capacitor and capacitance. The storage capacity of capacitance can be different from small to high storage.

Capacitance is nothing but the ability of capacitors to store energy in the form of electric charge. In simpler words, capacitance is the storing unit of the capacitor. Farad is the measuring unit of capacitance. 

Most capacitors usually contain two electrical conductors, and metallic plates separate them. Conductors can be in the form of electrolytes, a bead of metal or thin film, etc. 

Sometimes the shape of the capacitor also affects the capacitance. It depends on the distance between the plates and the area between the plates. The more distant the plates are, the more negative power will be charged. Moreover, positive plates will get easier to charge if the area is larger.  

Some factors can affect capacitance, such as plate spacing, area of plates, and dielectric. There are two types of variable capacitors. One is a tuning capacitor, and the other is a trimming capacitor.

Dimensional Analysis

Physical quantities are related to the dimensions of the measurement units used to define them. This helps us perform mathematical calculations that are easier, more precise, and quicker. In other words, it is the study of dimensional formulae. It is the technique used to manipulate dimensional formulae.

Before studying the dimensional formula, we should first understand dimensional constants:

The dimensional constants are the numbers that specify the dimensions of an object. In other words, they describe the shape and size of an object. The dimensional constants are written as a series of numbers separated by commas. Each number represents a value followed by a unit of measurement: D=1, m=metre, in=inch, ft=foot, yd=yard, km=kilometre, and so on. The first dimension constant, D, is used to specify the size of an object in terms of length.

Dimensions in units and measurements

The dimensions can be written as the powers of the fundamental units of length, mass, and time. It depicts their nature and does not show their magnitude.

Dimensional formula dimensional equation

The dimensional formula depicts the dependency of physical quantity with fundamental physical quantity and the powers.

Example

Let us take the formula of speed.

Speed = Distance / Time

The distance can be written in length [L]

Time can be written as [T]

The dimensional formula would be [ M0 L1 T-1]

Hence, we can conclude that the speed is dependent on only length and time, not mass.

Conclusion

A capacitor is a part of an electrical circuit used to temporarily store electricity between two parallel plates and is separated by a non-electrical circuit.

The electrical power in a capacitor is directly proportional to the applied voltage and counteracts the distance between the plates.

Only leakage current passes through the dielectric during the charging and discharging phases. It takes five times constant to charge or discharge a capacitor even if it is already somewhat charged.