Showing posts with label Capacitor. Show all posts
Showing posts with label Capacitor. Show all posts

Electrostatics Complete Lesson

Electrostatics is a branch of physics that deals with charges in the state of rest and its applications. Here in this chapter we are going to deal about charge, electric field, electric force between charges,electric intensity,electric potential,potential difference, electric potential energy,capacitor, capacity, effect of dielectric on the capacity and energy stored in capacitor etc. Detailed lessons are made about each of the topic and they are listed here below for the reference.

Electric Charge and Electric Force


Resultant Force and Coloumb's Law of Electric Force Problems and Solutions

Here are the further list of topics with complete lessons in this website.

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Energy Stored in Capacitor and Effect of Dielectric on it

Capacitor is a device used to store electric energy in it using the two plates. In storing the charge between the plates, we shall do some work and all that work done is stored in the form of energy between the plates.

To store small amount of charge, we shall do some small amount of work and it can be measured using the definition of potential. Any way that gives only small amount of work done. We need to store lot of small charges together in between the plates to get the total large charge. For doing that, we shall do large amount of work done. It is nothing but the sum of all small works done together. This can be obtained by integrating the basic equation as shown below.


Thus as shown in the above case, we can express the energy stored in a capacitor in the form of charge and potential. We can also express it in the form of capacity and voltage as  shown in the above diagram.

Effect of dielectric materiel on the energy stored of a capacitor

The effect of dielectric has to be studied in two possible different cases. The first case is when the dielectric is placed and battery connected to the system is disconnected. In this case, the charge in the capacitor remains constant and we shall use the energy equation in terms of charge and capacity. Of course the charge remains same and capacity increases by dielectric constant times. As a result, the total energy of the capacitor decreases by dielectric constant times.

In the second case, the dielectric material is placed and the battery is kept connected. As battery is still connected in the system, the voltage applied to the capacitor remains constant and its capacity increases by dielectric times. Thus here we shall use the energy stored in the capacitor in terms of capacity and voltage and hence total energy stored in the capacitor increases by dielectric constant times as shown below.


Problem and Solution

Here in the given problem number of capacitors are connected in parallel and their effective capacity is given. So that we can measure the individual capacity of the capacitor. Again it is given that the capacitors are connected in series and certain voltage is applied to the system. We need to measure the total energy stored in the system.

This can be done quite easily by first measuring the effective capacity of the system when they are connected in series. Then by applying the concept of energy stored in the capacitor, we can measure the energy as shown below.


Problem and Solution

This problem is not about capacity but rather about basic potential itself. A charged particle is moving under certain voltage and we need to measure the velocity acquired by it.

It can be solved quire easily using the concept of conservation of energy as shown below. The work done due to potential difference is actually converted into kinetic energy.


Problem and Solution

This problem is also not about capacity rather about electric potential and intensity. A charged particle of known mass is attached to a string and an electric field is applied to it. Now there is force to the field and gravitational force acting on the particle simultaneously. Thus the charged particle  turns an angle wit the vertical. We need to find the tension developed in the string and it can be done quite easily using the triangle law of vectors as shown in the diagram below.



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Capacitors in Series and parallel with Problems and Solutions

Capacitor is a device that is capable of storing energy and charge between its plates. We can connect the capacitors in different combinations.

Capacitors in Series

If one plate of the capacitor is connected to the other charged plate to the next capacitor and keep on connecting, this kind of connection is called series connection, When they are connected in series, the charge distribution on all of them is same but the total voltage connected to the system is shared across different capacitors basing on their capacity.

In series combination, total voltage of the system is the sum of all voltages shared across the system. We can find that the effective capacity of capacitors is less than any individual capacitors. It can be derived as shown below.



 Capacitors in Parallel

When capacitors are connected in parallel, the voltage shared across each capacitor is similar to the individual voltage on each capacitor. But the charge supplied to the system is shared across different capacitors based on their capacities.

If all positive plates of different capacitors are connected together and the negative plates of capacitors are also connected together, this kind of combination is called parallel combination.


When capacitors are connected they together can acquire a common potential as shown below. If different kind of plates are connected, the answer vary with the sign.


Problem and Solution

We know that when capacitors are connected in series, the effective capacity decreases and when they are connected in parallel, their effective capacity increases. If individual capacitors were need to be find out basing on total capacity of the systems when they are connected in series and parallel, we can find as shown in the problem below.


Problem and Solutions

When capacitors are connected in series, the charge across all the capacitors is same, but voltage is shared across them. We can find individual voltage as show in the diagram and problem with solution below.



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Working of Capacitor and Dielectric effect on Capacity

Capacitor is a device used to store the charge and its corresponding energy. Capacity is the ability of the device to store the charge. The charge stored in a device is directly proportional to the potential difference it has with the other parts from where the charge happens to flow. To eliminate the proportionality, a constant called capacity is used. And of course  it does not depend on the charge and potential difference and depends on the area of the plates and inversely proportional to the distance of separation between the plates.

Capacitors can be of different shapes and one of the popular one is parallel plate capacitor. It consists of two thin plates kept parallel to each other and there may be air or any non conducting materiel between them.It is measured with a SI unit called farad. 

Principle of working of a capacitor

Capacitor is a device which is used to store the charge in between the two parallel metallic plates. On one plate charge is allowed to accumulate and other plate is kept just next to it. The second plate is under the electric field influence of the first plate and hence, charges separation start happening in the second plate. This phenomenon is called electric charge induction.

Let the first plate is having positive charges. Because of induction, on the inner side of the second plate, negative charges are accumulated as the positive charges of the first plate attracts them.The positive charges on the second plate are repelled and hence they reach the outer side of the second plate.

Because of the inner charges of the second plate, it becomes easy for the new charges accumulation on the first plate and hence they help in storing more charge on the plate. But the second plates positive charges oppose any further loading of new positive charges on the first plate so that storing more charges turns more difficult.

Hence if we eliminate the outer positive charges of the second plate keeping the inner negative charges of it intact, it will help storing the more charge between the plates of the capacitor. That is the reason why the outer part of the second plate of the capacitor is connected to the earth. Thus all outer positive charges of the second plate goes to the earth and make the surface neutral. Hence we will be able to store more charge between the two plates at lower potential. This is how the capacitor is able to store charge between parallel plate capacitor.



Effect of dielectric material on capacity of a capacitor

In general the space between the two plates of capacitor is filled with air. If we place any non conducting materiel in between the plates, charges polarization happens in the atoms of it and hence generates a reverse potential in between. This further helps to store more charge in between the plates of the capacitor.


As the potential decreases, it automatically increases the capacity of the capacitor as  shown in the diagram below.


Basing on the definition of potential and capacity, we can prove that the capacity of a spherical capacitor is directly proportional to its radius as shown below.


Taking the same concept into consideration, we can measure the capacity of the earth capacitor assuming that the earth has a known radius 6400 KM. It is as shown below.


Effect  of dielectric on capacity of capacitor when it is partially filled

When a capacitor is filled with a dielectric partially such that it is filling the entire area but part of separation, it devises the capacitor into two capacitors connected in series. Thus we need to measure each capacity of the capacitor and need to add them basing on the rule of adding the capacitors in series. It is as shown in the diagram below.


Thus the effective capacity increases in this case also.

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