How Do We Find Out the Capacitance of a Parallel Plate Capacitor?

A capacitor is a device used to store an electric charge. From energy storage to electric noise filtering, capacitors are used in a wide range of activities in both industrial and daily life.

There are various types of capacitors categorized under two mechanical groups- fixed capacitors and variable capacitors. But for now, let’s talk about parallel capacitors and how do we find out the capacitance of a parallel plate capacitor.

You’ll get to know that in this article.

The Basics You Need to Know

Here, we’ll go through the basics first;

Parallel Capacitors

These have an assortment of electrodes. You’ll find 2 conducting plates acting as electrodes, and the dielectric you’ll see works as a separator. The plates are connected to the power supply.

And the plate that is attached to the positive terminal gets positive charge. Meanwhile, the plate that gets attached to the negative terminal gets negative charge.

An uncharged capacitor remains neutral when it is connected to a power supply, but stores charges as due to the attraction, opposite charges are trapped within the plates.

Capacitance

The capacitance of a capacitor is the ability to store an electric charge per unit of voltage across its plates, expressed as the ratio of the two. The unit of capacitance is Farad. Microfarad (µF) and picofarad (pF) are also widely used.

Factors Affecting Capacitance

How to Findout Parallel Plate Capacitor

Let’s learn about the factors affecting capacitance;

1. Area of Plates

As capacitance is measured across the surface of the plate, the physical size plays a huge role in determining the capacitance by a best capacitance meter. It is directly proportional to the (surface) area of the plates. A capacitor with a larger plate area can produce higher capacitance and vice versa.

But, in certain types of variable capacitors, if the plates are moved from a completely parallel position in relation to each other, the overlapping area changes. The new overlapping surface area then determines the effective plate area in calculating capacitance.

2. The Distance Between Plates

Capacitance is inversely proportional to the distance between the plates. With the increase of distance between plates, the ‘breakdown voltage’ increases; as it is directly proportional to the plate separation/distance between plates.

So, smaller capacitance is produced. Vice versa happens in case of decreasing the distance between the parallel plates.

3. The Dielectric Constant of the Material

The insulating material between the plates of a capacitor is called the dielectric. And the dielectric material can affect the voltage between the plates and influence changes in how much charge can be stored.

A material’s ability to store charges and establishing an electric field is known as dielectric constant or relative permittivity. It is denoted by εr. This constant is a relative ratio of the absolute permittivity of that matter (ε) and the absolute permittivity of vacuum (ε0), hence this is dimensionless and has no units.

It can be expressed by this formula: εr = ε / ε0. The value of ε0 is 8.85×10-12 F/m.

Capacitance is found to be directly proportional to this constant. Since this dielectric constant is calculated in ratio with the vacuum, the value taken is 1. In regular cases, we measure that of air, which is also close to a vacuum, hence close to 1.  

Calculating Capacitance

In this section, we’ll learn how to calculate capacitance.

General Equation

Since capacitance is the ratio of stored electric charge (Q) and the voltage across the plates or the potential difference between the two plates (V), we can simply write the formula as-

Capacitance, C = Q/V.

From this equation, we can also find charge (Q) and voltage (V) by rearranging the formula as Q = CV or V = C/Q.

The Equation for Parallel Plate Capacitors

For this kind, capacitance is found to be directly proportional to the size of the plates or plate area (A) and inversely proportional to the distance between the plates (d).

Capacitance is also directly proportional to the dielectric constant (ε0, when the plate is separated by air or empty space). So, we can write the capacitance of a parallel plate capacitor as-

C = Aε0 / d

Let’s dive deep into this equation.

According to the Gauss law, the electric field ‘E’ between the parallel plate capacitor can be written as- E= q/ A * ε0 …… (1)

The ‘potential difference’ between the parallel plates, is related to the electric field. It is defined as- V = Ed => E = V/d

Putting this value in equation (1), we get-

V/d = q / A * ε0

ð q / V = A * ε0 / d

ð C = A * ε0 / d

This is the expression we just learned for the capacitance of a parallel plate capacitor with free space as the medium between plates.

Learn the Extra Step: Multiple Parallel Plate Capacitor

A multiple parallel plate capacitor is where parallel plates are arranged with a dielectric material (other than air/empty space) between them in groups fitting each other.

This gives us two new things to take into consideration while calculating capacitance- dielectric constant of that material or relative permittivity of dielectric, and the number of plates.

C = (A * ε0 * εr / d) * (N – 1)

Where,

ε0 = Relative permittivity of a vacuum = 8.854 × 10-12 F/m

d = Distance between plates

N = Number of plates

εr = Relative permittivity of the dielectric

A = Area of each plate

Conclusion

We conclude this article with the hope and belief that together, we learned about parallel capacitors, capacitance, and how do we find out the capacitance of a parallel plate capacitor. Additional related topics have also been covered in a way that is easy to understand and remember!

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