Capacitors use non-conducting materials or dielectric, to store charge and increase capacitance. Dielectrics when placed between charged capacitor plates, it becomes polarized which reduces the voltage across the plate and increases the capacitance. In this article we will explore effect of dielectric on capacitance and basics of capacitor and dielectric. Also, we will discuss effect of dielectric on capacitance derivation, application of dielectric on capacitor and how dielectric increases the capacitance of capacitor. Let’s start our learning on the topic “Effect on Dielectric on Capacitance.”
What is Dielectric?
The materials that are very poor conductor of electric current but have the ability to store electric charges are called as dielectrics. The dielectric separates the metal plates of capacitor. A simple parallel plate capacitor, like two metal plates facing each other with air in between. When you charge it up, electrons pile up on one plate, creating a negative charge, while the other plate becomes positively charged. Some examples for dielectric materials, include ceramic, plastic, mica, glass etc.
Dielectric Constant
The ratio of the permittivity of the substance to the permittivity of the free space gives the dielectric constant. It is denoted by k.
Dielectric Constant Formula
The dielectric constant formula is mathematically expressed as:
k = ϵ / ϵo
where,
- k is the dielectric constant
- 𝜺 is the permittivity of the substance.
- 𝜺0 is the permittivity of the free space.
What is Capacitance?
The capacity of a conductor to store charge inside it is known as the capacitance of the conductor. We can also say that the amount of the storage of the conductor to store charge is called capacitance.
Capacitor Definition
The conductors which are used for storing the charge are referred to as capacitors. They are used to store electric energy in the form of electric charges. They are generally composed of two plates separated by an insulating medium. Where one plate is positively charged and the other is negatively charged.
Capacitance Formula
Capacitance is represented by C and it is the ration of the charge stored on the capacitor plates to the voltage.
C = Q/V
where,
- Q is the electric charge
- C is the capacitance
- V is the voltage across the plates
Unit of Capacitance
The unit of capacitance is the Farad, which is given after the English physicist and chemist Michael Faraday.
Conversion of Unit
- Microfarad (μF) 1μF = 1/1,000,000 = 0.000001 = 10-6 F
- Nano-farad (nF) 1nF = 1/1,000,000,000 = 0.000000001 = 10-9 F
- Picofarad(pF) 1pF = 1/1,000,000,000,000 = 0.000000000001 = 10-12 F
Effect of Dielectric on Capacitance
The dielectrics are the material which is either insulators or very poor conductor of electric current. We will look into how the value of capacitance changes when we place a dielectric material between the plates of the capacitors.
In parallel plate capacitors the two plates are usually separated by a dielectric. They can be completely or partially, depending on the gap between the boards. When there is a dielectric between the two capacitor plates of a parallel plate capacitor, the electric field polarizes the dielectrics.
Derivation
Assume there are two plates are kept parallel to each other separated be a distance d and cross-sectional area of each plate is A. Now we will calculate the value of the capacitance due to this parallel plate capacitor which is given by C.
Step 1: Electric field by a single thin plate.
The electric field (E′) produced by a single thin plate can be found using Gauss’s law. For a uniformly charged plate with surface charge density (σ), the electric field just outside the plate is:
E′= σ / 2ϵo
Step 2: Total electric field between the plates.
When you have two parallel plates, each with the same surface charge density (σ), the total electric field (E) between them is the sum of the electric fields produced by each plate. Since both fields are in the same direction and have the same magnitude, we simply add them up. Total electric field between the plates
E = σ/2ϵo+σ/2ϵo
or
E = σ/ϵo
Step 3: Electric potential difference (Voltage) between the plates.
The potential difference (V) between the plates is the work done per unit charge to move a positive test charge from one plate to the other. For a uniform electric field (E), the potential difference (V) between two points separated by a distance (d) is given by:
V = Ed
Step 4: Now for Capacitance (C).
The capacitance (C) of a parallel plate capacitor is defined as the ratio of the charge (Q) stored on one plate to the potential difference (V) between the plates is given by:
C = Q/V
Step 5: Combining equations for capacitance.
Substitute the expressions for electric field (E) and potential difference (V) into the capacitance formula:
As we know that σ = Q/A, then E = Q/Aϵo
Potential difference between the plates V = Ed
V = Qd / Aϵo
Capacitance C = Q/V
Thus, we get capacitance of parallel plate capacitor C = Aϵo/d
where, A = area of the plate and d = distance between them
Now when we introduced any dielectric material the formula changes to
C = Aϵok/d
or
C = kC0
where k is the dielectric constant of the material.
So, when the value of k increases the value of capacitance too increases and vice-versa
The value of Capacitance is directly proportional to the dielectric constant.
C ∝ k
To increase the capacitance of the parallel plate capacitor, a dielectric may be present between the plates because its relative permittivity K is greater than 1.
Application Of Dielectrics in Capacitors
- Capacitor Functionality: Dielectrics are widely used in capacitors to store energy in an electric field between plates.
- Signal Filtering: They help filter out unwanted signal noise in resonant circuits.
- Power Burst: Dielectrics can provide a quick burst of power to other components.
- Desirable Features: High electrical resistivity and low dielectric loss are important characteristics because dielectrics primarily work as insulators rather than charge retainers.
- Insulation: Dielectrics are commonly used for insulating wires, cables, and similar applications.
- Sensor Technology: Dielectrics is also used in in sensor technology.
How Dielectric Increase the Capacitance of a Capacitor
When a dielectric material is inserted between the plates of a capacitor, it increases the capacitance of the capacitor. This increase occurs due to the effect of the dielectric material on the electric field and the polarization of the material.
Polarization of Dielectrics
When a dielectric material is placed on the grid of a capacitor, it contains atoms or molecules that can be polarized in the presence of an electric field. An external electric field induces a dipole moment in the atoms or molecules of the dielectric material. It can be seen that the induced dipoles are coupled with the electric field.
Polarization of electric field
Increase in Capacitance
Since capacitance (C) is defined as the ratio of the charge stored on the plates to the potential difference between the plates (Q/V), a decrease in the electric field (E) between the plates leads to an increase in capacitance. Mathematically, capacitance is directly proportional to the permittivity of the material (ϵ) and the area of the plates (A) and inversely proportional to the distance between the plates (d). Then whenever a dielectric material is placed the value of permittivity is affected according to the formula and thus there is increase in capacitance.
Conclusion
From the above discussion we can conclude that the capacitance and the dielectric constant is directly proportional to each other. There are various advantages of using these dielectrics between the plates of the capacitors. Using the relation between capacitance and dielectric constant we can easily determine how the value of capacitance rely on the dielectric constant. It decreases the voltage across the plates of the capacitor hence, increasing the capacitance.
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FAQs on Effect of Dielectric on Capacitance
What is capacitance?
Capacitance refers to the ability of a conductor to store charge within it. It’s defined as the amount of charge that a conductor can store per unit voltage.
What is the formula and unit of capacitance?
Capacitance (C) is calculated as the ratio of charge (Q) stored on the plates to the voltage (V) across them, expressed as C = Q/V. The unit of capacitance is the farad (F).
How does a dielectric affect capacitance?
When a dielectric material is inserted between the plates of a capacitor, the capacitance increases. This is because the dielectric enhances the electric field, effectively boosting the capacitor’s ability to store charge.
What is the formula of effect of dielectric on capacitor?
The formula of effect of dielectric on capacitor is given by: C = kC0
What is the dielectric in a capacitor?
The insulator material between the plates of capacitor is called as the dielectric of a capacitor.