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The parallel plate capacitor helps to understand the potential that changes according to the charge passed. The parallel plate capacitor calculation is simple and resolvable. Before understanding the deep functionalities, we should know the parallel plate capacitor’s meaning and its importance in detail. Then we can arrive to determine the formula of a parallel plate capacitor.
What is a Parallel Plate Capacitor?
Parallel plate capacitors have electrodes and insulating material to form sequences. It can store a finite, limited amount of energy. If a battery is connected across two parallel plates, the plates are charged and form an electric field. This process is called a parallel plate capacitor.
If more charge is supplied between the parallel plates, then the potential will be increased, and it will provide charge leakage straight away. And if we place another plate next to the positively charged plate, then the negative charge flows in the direction of the positively charged plate.
Since both the plates have charges, plate 2’s negative charge reduces the potential difference on plate 1, whereas plate 2’s positive charge increases the potential difference on plate 1. More charge will be provided to plate 1 because of the negative charge impact on plate 2. So, the potential difference is less on plate 2.
Parallel Plate Capacitor Formula
The direction of the positive test charge is called the direction of the electric field. The change in electric charge concerning the electric potential is called capacitance. And the capacitance acts as a body to store all the electric charges.
Consider the parallel plate capacitor consists of two plates and the area is A, the distance between the plates is “d”.
The formula to determine the parallel plate capacitor is
C=kϵ0A/d
ϵo is the permittivity of space, i.e. (8.854 × 10−12 F/m)
k is the relative permittivity
Parallel Plate Capacitor Derivation
The figure below depicts a parallel plate capacitor. It has two large plates placed parallel to each other at a distance “d”.
The plates’ distance is smaller than the area of the conductive plate. So, it is called infinite plane sheets. The charge density can be determined using the below formula
For plate 1:
Let us separate the regions of the parallel plate capacitor for calculation purposes,
Area 1 – the left area to the plate 1
Area 2 – the area between the plate 1 and 2
Area 3 – The right area of plate 2
Calculation of electric field around parallel plate capacitor:
For Area 1, The magnitude will be the same because of the infinite plane sheets. Since the plane sheets’ direction is placed opposite each other, the electric field will become 0.
For Area 2, The magnitude and the electric field’s direction are the same. So, the equation will be
For Area 3, the magnitude is the same as that of area 1. So the electric field is generated because of the plane sheets present in that region.
If the direction of the electric field is from positive to negative plate and if it is uniform in nature, then the potential difference is calculated by using the distance created between the two plates with respect to the electric field generated.
Let’s see some examples for better understanding
Example 1
A parallel plate capacitor kept in the air has an area of 0.50m2 and the distance between the plates 0.04m. Estimate the parallel plate capacitor.
Solution:
Given:
Area A = 0.50 m2,
Distance d = 0.04 m,
relative permittivity k = 1,
ϵo = 8.854 × 10−12 F/m
The parallel plate capacitor formula:
C=kϵ0A/d
= 8.854×10−12 × 0.50 / 0.04
= 4.427 x 10−12 / 0.04
So, C = 110.67 x 10−12 F
Example 2
Calculate parallel plate capacitor’s area in the air by considering the capacitance as 25 nF and distance between the plates is 0.04m.
Solution:
Given:
Capacitance = 25 nF,
Distance d = 0.04 m,
Relative permittivity k = 1,
ϵo = 8.854 × 10−12 F/m
The parallel plate capacitor formula
C=kϵ0Ad
A=dCkϵ0
= 0.04 × 25×10−9 / 1×8.854×10−12
A = 1 x10−9 / 8.854 ×10−12
So, the area of the parallel plate capacitor is 112.94 m2.
Conclusion
The parallel plate capacitance depends on the distance between the plates and the area. The single capacitor cannot store the high electric charge, so two parallel plates are needed to store a high amount of electric charge. The parallel plate capacitors are mostly used in DC power supplies, automobile industries etc. Each application has various advantages and characteristics related to capacitance. Calculation of capacitance is nothing but measuring the capacitor’s capability to store energy in the form of charge. The parallel plate capacitor is mainly used to store a large volume of electric charge. The single capacitor can hold only a few amounts of electric charges.
In contrast, the two parallelly placed plates create an electric field when connected to the battery and store a huge amount of electric charge. The calculation and importance of parallel capacitance have been explained in detail. Mostly parallel plate capacitor jee notes are famous among the students who prepared for jee examinations.
