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Parallel Plate Capacitor

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Parallel Plate Capacitor

A parallel plate capacitor has two conducting plates with the same surface area, which act as electrodes. One plate acts as the positive electrode, while the other one acts as the negative electrode when a potential difference is applied to the capacitor. The two plates are separated by a gap that is filled with a dielectric material. Dielectric materials are electrically insulating and non-conducting, which means that they do not conduct current and can hold the electrostatic charges while emitting minimal energy in the form of heat or leakage currents.

Dielectric materials have the ability of electric polarisation.

Electric polarisation is the tendency of a material’s molecules to obtain an electric dipole moment when the material is placed in an external electric field.

How does a parallel plate capacitor work?

The electrical charges of the material are separated proportionally to the electrical field, creating two poles, a negative and a positive one.

The electric polarisation process is similar to magnetisation, where a magnetic dipole is induced in a magnetic material when placed near a magnet.

Therefore, when dielectric materials are placed in an external electrical field, the dipole moment that is induced per unit volume of the dielectric material is also known as electric polarisation. This is described by the equation below, where k is the dimensionless dielectric constant, E the permittivity of the material, and Eo the permittivity of vacuum, which is around 8.85 × 10-12 farad per metre (F/m).

The two plates of the parallel plate capacitor are connected to a power supply. The plate that is connected to the positive terminal of the battery acquires a positive charge, while the plate that is connected to the negative terminal acquires a negative charge. This happens because the positive pole pushes electrons to the opposite plate. Due to the attraction between the positive and negative charges acquired in the positive and negative plates, the charges are stored within the plates of the capacitor.

Electric field lines are formed between the two plates from the positive to the negative charges, as shown in figure 1. The polarisation of the dielectric material of the plates by the applied electric field increases the capacitor’s surface charge proportionally to the electric field strength in which it is placed.

Parallel Plate Capacitor, Parallel plate capacitor configuration, StudySmarterFigure 1. Parallel plate capacitor configuration. Source: toppr.com.

As both plates have charges, the negative charge on one of them reduces the negative charge of the other. On the other hand, the positive charge on one of the plates increases the potential difference between the plates. However, the negative charge on the negatively charged plate has more impact, so more charge can be given to the positively charged plate. When a voltage V is applied to the capacitor, a charge Q is stored. This is the principle of the parallel plate capacitor.

Parallel plate capacitor: Derivation

The two plates of a parallel plate capacitor are separated by a distance d measured in m, which is filled with atmospheric air. The cross-sectional area of each plate A is measured in m2. The electric field E of each plate is equal to the following, where σ is the surface density.

If the potential difference between the two plates is equal to V, when we substitute the equation found for the electric potential, we get:

Now, substituting the capacitance in the derived voltage, we get:

It can be seen that the capacitance depends on the distance between the plates. The charge stored is proportional to the surface area and inversely proportional to distance. This can also be validated by considering the characteristics of the Coulomb force, where like charges repel and unlike charges attract each other. The force between charges decreases with distance. The bigger the plates, the greater the charge storing capacity as the charges spread out more. Thus, the storable charge is increased when the area is also increased. Similarly, the closer the plates, the greater the attraction force between the opposite charges, so capacitance should be greater when the distance is decreased.

Parallel Plate Capacitor: Leakage currents

A given charge is supplied to each plate. Because there is no ideal dielectric material that can hold the charge perfectly, the increase in the potential leads to leakage currents, which cause the capacitor to discharge in an unwanted way once it is disconnected from the circuit.

The amount of time a capacitor can hold a charge depends on the quality of the dielectric material used in the capacitor.

Parallel plate capacitor: Electric field

In a parallel plate capacitor, when a voltage is applied between two conductive plates, a uniform electric field between the plates is created. However, at the edges of the two parallel plates, instead of being parallel and uniform, the electric field lines are slightly bent upwards due to the geometry of the plates. This is known as the fringing or edge effect (see figure 2).

A capacitor’s electric field strength is directly proportional to the voltage applied while being inversely proportional to the distance between the plates.

Parallel Plate Capacitor, Fringing of the electric field at the edges of the two plate, StudySmarterFigure 2. Diagram showing the fringing of the electric field at the edges of the two plates.

Usage of parallel plate capacitors

The usage of capacitors range from filtering static out of radio reception to energy storage in heart defibrillators and include the following:

  • Energy storage and circuit protection against unusual spikes in voltage or any interruption in the circuit.
  • Electronic signal processing.
  • Suppression and coupling.
  • Motor starters used in pumps and compressors such as refrigerator compressors.

The reason capacitors cannot be used like batteries is that they cannot hold energy for a long time due to the leakage currents.

You can make a parallel plate capacitator at home using two sheets of paper, which are glued together, with an aluminium foil sheet on glued to each side of the paper. Then you need to attach copper wires to the upper right and bottom left corners and connect each wire to the electrodes of a battery.

A parallel plate capacitor has a capacitance of 5 mF. Determine the capacitance after the distance between them is reduced to a third of the initial distance, and with the space between the two plates having a dielectric constant of 7.

Solution:

We derive an expression relating the given capacitance and the new capacitance with the reduced distance.

A squared length capacitor is a capacitor that has the same width and length. Hence, its area can be calculated by the squared length.

Determine the area of the capacitor if the potential difference between the plates is 0.5 V, the distance between the plates is 3mm, and a charge of 1.2 ⋅ 10-9 C is stored in the capacitor.

Solution:

We use the equation that relates the potential difference with the area. Then we substitute using the given values in SI units.

Parallel Plate Capacitor - Key takeaways

  • A parallel plate capacitor is a device that stores charge.
  • Parallel plate capacitors feature two plates made from conductive materials.
  • Capacitors store charge by electric polarisation.
  • Parallel plate capacitors have a wide range of applications, such as motor starters, signal processors, compressors, etc.

Frequently Asked Questions about Parallel Plate Capacitor

A parallel plate capacitor is a type of capacitor that is constructed by two parallel conducting plates and a dielectric material between them.  It can be used to store electrical energy and signal processing.

We can increase the capacitance of a parallel plate capacitor by increasing the area of the plates or decreasing the distance between the plates.

A parallel plate capacitor stores electrical charges when there is a voltage difference between the plates. Because there is a dielectric material between the plates, the electrical charges will be stored in the dielectric material.

Final Parallel Plate Capacitor Quiz

Question

What is a parallel plate capacitor?

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Answer

A capacitor is a device used to store electric charge.

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Question

List three applications of a parallel plate capacitor.

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Answer

  • Energy storage.
  • Electronic signal processing.
  • Pulsed power and weapons.

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Question

Which of the following applications is not an application for a parallel plate capacitor?

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Answer

Battery manufacturing.

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Question

What is the main working principle of a parallel plate capacitor?

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Answer

Electric polarisation.

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Question

What is electric polarisation?

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Answer

It is the tendency of a material’s molecules to obtain an electric dipole moment when the material is placed in an external electric field.

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Question

What materials are the plates made of?

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Answer

Dielectric materials.

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Question

What are dielectric materials?

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Answer

Materials that have the ability of electric polarisation.

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Question

What is the configuration of a parallel plate capacitor?

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Answer

A parallel plate capacitor consists of two identical conducting plates connected to the electrodes of a battery. The two plates are separated by a gap that features a dielectric material.

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Question

What is a charge leakage?

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Answer

When the amount of the supplied charge exceeds a certain limit, the potential increases, which could potentially lead to a leakage in the charge.

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Question

What is fringing?

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Answer

It is the divergence of the electric field lines around the edges of the plates.

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Question

How can we construct a parallel plate capacitor?

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Answer

Using two aluminium foil layers sandwiched between two paper sheets.

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Question

What charge is stored in a 100 μF capacitor when 120 V is applied to it?

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Answer

0.012C.

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Question

Calculate the voltage applied to a 3 μF capacitor when it holds 5 μC of charge.

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Answer

1.66V.

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Question

How would you decrease the energy capacity of a capacitor?

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Answer

By decreasing the area or increasing the distance between the two plates.

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