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.
Effect of Dielectric on Capacitance
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.”