## What is a Parallel Plate Capacitor : Principle & Its Derivation

- Frank
- Jun 01, 2022
- read:

The capacitor is one kind of electrical component and the main function of this is to store the energy in an electrical charge form and generates a potential difference across its two plates similar to a mini rechargeable battery. Capacitors are available in different types from very small to large but the function of all these is the same as storing electric charge. A capacitor includes two metal plates that are separated electrically through the air or good insulating material like ceramic, plastic, mica, etc. This insulating material is known as a dielectric. This article discusses an overview of the parallel plate capacitor and it’s working.

### What is a Parallel Plate Capacitor?

**Definition:** A capacitor that can be formed using the arrangement of electrodes and insulating material like dielectric is known as a parallel plate capacitor. The capacitor includes two conducting plates which are separated through a dielectric material. Here conducting plates acts as electrodes.

### Parallel Plate Capacitor Construction

The construction of this capacitor can be done with the help of metal plates otherwise metalized foil plates. These are arranged in parallel to each other with equal distance. The two parallel plates in the capacitor are connected to the power supply. When the primary plate of the capacitor is connected to the +Ve terminal of the battery then it gets a positive charge. Similarly, when the second plate of the capacitor is connected to a negative terminal of the battery then it gets a negative charge. So it stores the energy between the plates because of the attraction charges.

### Circuit Diagram

The following circuit of a parallel plate capacitor is used to charge the capacitor. In this circuit, ‘C’ is the capacitor, the potential difference is ‘V’ and ‘K’ is the switch.

Once the key like ‘K’ is closed, the flow of electrons from the plate1 will start flowing in the direction of the +Ve terminal of the battery. So the flow of electrons will be from –Ve end of the battery to +Ve end.

In the battery, the flow of electrons in the direction of the positive end, after that they will start flowing in the plate2. Like this, these two plates will get charges, where one plate will get a positive charge and the second plate will get a negative charge.

This procedure will continue once the capacitor gets a potential difference in the precise amount of the battery. Once this process stops, then the capacitor stores electric charge including the potential difference. The charge in the capacitor can be written as Q = CV

### Principle of Parallel Plate Capacitor

We know that we can supply a certain amount of electric charge to a capacitor plate. If we provide more energy, then there is an increment in the potential so that it leads to an outflow in the charge. Once the plate2 is arranged next to the plate1 which gets a positive charge, then a negative charge will be supplied to this plate2.

If we get plate2 and it is placed next to the plate1, then negative energy can be supplied through the plate2. This negatively charged plate is nearer to the positively charged plate. When plate1 & plate2 have charges, then the negative charge on the plate2 will decrease the potential difference on the first plate.

Alternatively, the positive charge on the second plate will raise the potential variation on the first plate. However, the negative charge on plate 2 will have an extra impact. Thus, more charge can be given on plate 1. So the potential disparity will be less because of the negative charges on the second plate.

### The Capacitance of the Parallel Plate Capacitor

The electric field direction is nothing but the flow of the positive test charge. The limitation of the body can be used to store the electric energy is known as capacitance. A capacitor includes its capacitance similarly, the parallel plate capacitor includes two metallic plates with area ‘A’, and these are separated through the’ distance. The parallel plate capacitor formula can be shown below.

**C = k*ϵ0*A*d**

Where,

‘ϵo’ is the permittivity of space

‘k’ is the dielectric material’s relative permittivity

‘d’ is the partition between the two plates

‘A’ is the area of two plates

### Parallel Plate Capacitor Derivation

The capacitor with two plates arranges in parallel is shown below.

The first plate in the capacitor carries ‘+Q’ charge and the second plate carries ‘–Q’ charge. The area between these plates can be denoted with ‘A’ and the distance(d). Here, ‘d’ is smaller than the area of the plates (d<<A). When the whole charge on the first plate is ‘Q’ & ‘A’ is the area of the plate, then the density of surface charge can be derived as

**σ =Q/A**

Similarly, when the whole charge on the second plate is ‘-Q’ & is the area of the plate is ‘A’, then the density of surface charge can be derived as

**σ = -Q/A**

The regions of this capacitor can be divided into three divisions like area1, area2, and area3. Area 1 is left to the plate1, area 2 is between the planes & area 3 is the right of the second plate. The electric field can be calculated in the region around the capacitor. Here, the electric field is consistent & its path is from the +Ve plate to the –Ve plate.

The potential difference is calculated across the capacitor by multiplying the space between the planes with the electric field, it can be derived as,

**V = Exd = 1/ε(Qd/A)**

The capacitance of the parallel plate can be derived as **C = Q/V = εoA/d**

The capacitance of a parallel plate capacitor with 2 dielectrics is shown below. Each plate area is Am2 and separated with d-meter distance. The two dielectrics are K1 & k2, then the capacitance will be like the following.

The capacitance of primary half of the capacitor width is **d/2 = C1=> K1Aϵ0/ d/2=> 2K1Aϵ0/d**

Similarly, the capacitance of the next half of the capacitor is **C2 = 2K2Aϵ0/d**

Once these two capacitors are connected in series then the net capacitance will be

**Ceff= C1C2/C1+C2= 2Aϵ0/d( K1K2/ /K1+K2)**

### Parallel Plate Capacitor Uses / Applications

The applications of the parallel plate capacitor include the following.

- By connecting different capacitors in parallel in a circuit, then it will store more energy because the resultant capacitance is the number of individual capacitances of all the types of capacitors within the circuit.
- Parallel plate capacitors are used in DC power supplies to filter the o/p signal & remove the AC ripple
- The capacitor banks for energy storage can be used in PF(power factor) correction using inductive loads.
- These are used in automobile industries for regenerative braking within huge vehicles.

### FAQs

**1). What is a parallel plate capacitor?**

When two metal plates are connected in parallel by separating with a dielectric material is known as a parallel plate capacitor.

**2). How can we calculate the capacitance of a parallel plate capacitor?**

The capacitance of this capacitor can be calculated by using this formula like C = ε(A/d).

**3). What is the SI unit of a capacitor**

The SI unit is the farad (F).

**4). What does the parallel plate capacitor’s capacitance depend on?**

It depends on the distance and the area of the two plates.

Thus, this is all about an overview of the parallel plate capacitor. Whenever the high amount of electric charge needs to store in a capacitor, it is not possible within a single capacitor. So a parallel plate capacitor is used to store a high amount of electric energy as they use two plates like electrodes. Here is a question for you, what are the advantages and disadvantages of a parallel plate capacitor?