Effects of Dielectrics in Capacitors

We know that the gap between the parallel plates of a capacitor can be empty and filled with air. Suppose that the dielectrics such as mica, paper and glass are welcomed amid the plates and consequently, the capacitor’s capacitance is altered.

Effects

Dielectric can be put inside the plates in two dissimilar ways. These situations are as follows:

• When the capacitor is detached from the battery

• When the capacitor is attached to the battery

When the Capacitor is Detached from the Battery

Let’s assume that a capacitor has two parallel plates, each with a cross-sectional area ‘A’, . These plates are divided with the help of a specific distance ‘d’. The capacitor is charged using a battery with voltage ‘V₀’, and the stored charge is ’Q₀’. Moreover, the battery gets disconnected from the capacitor, and the dielectric is put between the plates. The introduction of the dielectric among the plates will decrease the electric field.

Here, E₀ represents the electric field in the capacitors. At the same time, there is the absence of a dielectric, and ε_r is said to be the relative permeability of the dielectric or usually known as the dielectric constant.

While ε_r > 1, then, electric field ‘E’ < ‘E₀. Therefore, the electrostatic potential variation among the plates ‘V = Ed’ also gets reduced. However, at that time only, the charge ‘Q₀’ will remain constant after the battery gets detached.

We all have studied that the capacitance is inversely proportional to the potential difference. Hence, as ‘V’ is being reduced, ‘C’ will increase. As ε_r > 1, we have ‘C’ > ‘C₀’. Therefore, the insertion of the dielectric constant εr causes the growth of the capacitance. Here ε_r = ε_rε₀ is the dielectric medium’s permittivity.

Once the dielectric is inserted, the charge Q₀ stays constant. However, the capacitance starts growing. Consequently, the energy that is stored starts decreasing. As ε_r > 1, we will be getting U < U₀. Moreover, there is a fall in the amount of energy because, when the Dielectric is inserted, the capacitor wastes a bit of energy in pulling inside the Dielectric.

When the Capacitor is Attached to the Battery

Let us now talk about what happens when the battery of voltage ‘V₀’ stays attached to the capacitor when the dielectric is put inside the capacitor. Moreover, the potential difference ‘V₀’ remains the same across the plates. As an outcome, it is seen that when the dielectric is put inside, the charge that is stored in the capacitor gets increased through εr as well and because of this increased charge, the capacitance also gets increased. Hence, the reason behind the increase in capacitance is different in this case as compared to the case when the battery is detached before introducing the dielectric.

Notably, we didn’t use the expression because, here, the charge and the capacitance are altered. Whereas in the other equation, the ‘V₀’ stays the same. The capacitance starts increasing once the Dielectric is put inside. Therefore, it also increases the energy that is already stored. As ε_r > 1we will be having ‘U’ > ‘U₀’. It might be noticed here that since the voltage amid the ‘V₀’ capacitor is the same, the electric field also remains the same between the plates. Moreover, here, ε is the permittivity of the provided dielectric material.

Effect of Dielectric on Capacitance

The dielectrics are generally located between two plates of the parallel plate capacitors. They can occupy the region among the plates or can occupy it partially. Moreover, when the dielectric is put among the 2 plates of the parallel plate capacitor, it gets polarised through the available electric field. Furthermore, the surface charge densities are considered as σp as well as – σp. When the dielectric is placed totally among the 2 plates of the capacitor, its dielectric constant starts increasing from its vacuum value.

How does Dielectric Increase the Capacitance of the Capacitor?

The capacitance ‘C’ of the capacitor is directly proportional to the electric field created between the plates of the parallel plate capacitor. Because of the presence of the dielectric, the strength of the electric field gets reduced, as well as if the overall charge on the plates is kept the same. Then the potential difference decreases across the capacitor plates. In the same way, the dielectric causes the growth of the capacitor’s capacitance.

The Capacitance of a Parallel Plate Capacitor with a Dielectric Slab

Parallel plate capacitors comprise a dielectric slab of the dielectric constant ‘K’ among its plates that covers thirteen of the areas of its plates. Moreover, the whole capacitance is ‘C’, whereas the portion with the dielectric in between is ‘C1’.

Conclusion

This study material concludes that the dielectrics, for example, mica, paper, glass, etc., are introduced amid the plates and then there occurs a change in the capacitance of the capacitor. Moreover, various effects on the dielectric in the capacitors are discussed in the article that will make everything clear about this topic and talk about the effects of dielectric on the capacitance.