Energy Stored in Capacitor Equation

Introduction to Energy Stored in a Capacitor Equation

Capacitance:

Different conductors have different capacities to hold electric charge. The capacity of a conductor to hold charge depends upon the shape, size and surroundings of the conductor. The capacity of a conductor to hold charge is called capacitance.I like to share this paper capacitor with you all through my article.

For an isolated conductor when we increase the charge on the conductor, its potential also gets increased. The charge on the conductor is directly proportional to the potential of the conductor.

Q a V

Q = CV

Here C is proportionality constant called as capacitance. So capacitance is

C = Q / V

Unit of capacitance is coulomb / volt or farad.


Energy Stored in a Capacitor Equation:

Consider an uncharged capacitor of capacitance C. The capacitor is charged to a potential V when connected to a battery. Let the charge on the capacitor is Q. Suppose at any intermediate state of charging, let the instantaneous charge on the capacitor be q and potential difference across the capacitor is

dV = q /C. The work done to increase the charge dq is given as

dW = dV.dq

= (q /C) dq

The total work done to charge the capacitance from q = 0 to final charge

q = Q is i. e. is the energy stored in capacitor.

W = ? (q/C) dq

= (1/C) (Q2/2)

= Q2 /2C ……….. (1)

= (CV)2 /2C

U = (1/2)CV2 ……….. (2)

Equation (1) & (2) are the relation for energy stored in capacitor.


Effect of Dielectric on Energy Stored in a Capacitor on Equation:

1) When a charging battery is removed from the capacitor and dielectric of constant k is added, then the energy stored in the capacitor decreases by k times.

2) When a dielectric of constant k is added keeping the charging battery connected to the capacitor, then the energy stored in the capacitor increases by k times.

Electric Flux Density

Introduction to electric flux density:

The electric field creates a force on a charge and hence the charge moves along a certain path called the electric flux line. Also the force between two charges acts along a certain path. This path is also called the electric flux line. The electric flux through a surface held inside an electric field represents the total number of electric lines of force crossing the surface in a direction normal to the surface. it is denoted by  ?.

Magnitude of flux depends only on the charge from which it originates. The flux lines are equal to the charge in Coulombs. It is only an imaginary line.  Its direction is same as that of the electric field. It is a scalar quantity.

Electric Flux Lines

Electric flux lines from a point charge:

Electric flux lines between a positive charge and a negative charge:

Electric Flux Density:

1. Electric flux density is defined as the electric flux crossing the surface area.

Mathematically, Electric flux density,  D is defined as

D = ??/ ?S  ,   C/m2

Where, ? is electric flux crossing the differential area, ?S.

The direction of ?S is always outward, normal to ?S, that is, ?S = ?S an .

2. Electric flux density is also defined as (in a general medium)

D = eE , C/m2

Where e is permittivity, F/m

E is electric field strength, V/m

3. Electric flux density in a dielectric medium is given by

D = e0E + P


Where P is polarization of medium

e0 is permittivity of free space.

4. Electric flux density is a vector quantity.

5. The unit of electric flux density is C/m2.

6. In free space, D is in the direction of E.

7. D, in a Gaussian surface, is determined from gauss’s law.

8. D is independent of the medium. 

Heating Effects of Electric Current

Introduction to heating effects of electric current:

When we apply potential difference accross two ends of wire, an electric is set up in the wire.  Such a current is due to motion of free electrons in the wire.  During the motion of electrons they collide with each other and also with ions in the wire.  Due to these collisions kinetic energy of electrons decreases.  This loss in kinetic energy appears as heat and temperature of wire rises.  The amount of heat produced depends on (1) the current passing through the wire  (2) the resistance of the wire and 3) time for which current is passed.
Having problem with Electric Dipole Moment keep reading my upcoming posts, i will try to help you.
The amount of heat produced in a conductor is given by the formula H =I2Rt  Joules, where I is the current flowing through the conductor, R is the resistance of the conductor and t is the time for which the current passes through the conductor.

This mathematical equation can be stated in the form of a law which is known as Joule's law.

It states that " the quantity of heat generated (H) in a conductor of resistance (R), when current (I) flows through for time (t) is directly proportional to

i)  the square of the current

ii) the resistance of the conductor

iii) the time for which the current flows.

Applications of Heating Effect of Electric Current:

The heating effect of electric current has many practical applications.  It is used in many domestic appliances such as an electric heater, an electric iron, a geyser, lectric oven etc.

1)  An electric bulb contains a thin filament of metal like tungsten.  It has high melting point.  When current passes through the filament it is heated to high temperature and emits light.  This is the principle on which electric incandescent light bulb works.

2)  An lectric iron used for ironing clothes consists of a coil of high resistance covered by insulating mica sheets and kept inside heavy metal block.  When electric current passes through the coil it gets heated.  The iron metal block gets heated and can be used for ironing clothes.

3)  An important application of heating effect of electric current is a safety device known as "fuse".  Fuse is usuaaly made up of alloys of lead and tin.  It has very low melting point.  It melts with small rise in temperature.  Its diameter is such that it melts when a current passing through it exceeds certain value.  When excess current passes through fuse due to some accident such as short circuit, the wire melts and circuit immediately breaks down.  When shorcircuit occurs, high current flows through the circuit, the fuse wire gets heated up and melts.  The cicuit is broken and current stops flowing.


4) In industry soldering, welding, cutting, drilling and working of electric furnaces are based on heating of electric current.

5) In surgery, a fine heated platinum wire is used for cutting tissues much more efficiently than knife.

Different Sources Of Energy

Different Sources Of Energy

In our daily lives, we use energy for doing work, which is taken from various sources. For instance, we use energy to lift a box or use an electrical energy to light a lamp, etc. The different form of energies like muscular energy, electrical energy, chemical energy, heat energy, kinetic energy, etc. comes from various sources. A good source of energy would be one which would do a large amount of work per unit volume or mass, easily accessible , easy to store and transport, and economical.

There are two forms of energy, renewable and non -renewable energy.

A non-renewable resource cannot be produced,regenerated, or reused . These are limited.
A renewable resource can be produced and reused.

In ancient times, wood was the most common source of heat energy, while energy of flowing water and blowing wind was used for various purposes. The need for energy was high, as we entered into the industrialization era. This led us to find new forms of energy for the betterment of all life forms over the world. The growing demand of energy was met by the fossil fuels-coal and petroleum. These are formed from millions of years ago and it is limited. These fuels which are non-renewable sources of energy should be saved and conserved. These fossil fuels are burnt every day in power stations to heat water and to generate electricity. Here the process of converting heat energy  into electrical energy takes place.

The Various other Sources of Energy

The various renewable sources of energy are the following:-

1.Solar energy

2. Wind energy

3.Rain

4. Tidal energy

5.Geothermal energy

6.Hydrothermal energy

Hydro Power Plants:-

            The Kinetic energy of flowing water or the potential energy of the water at a height is converted into electrical energy in the Hydro-power plants. This energy is used for various purposes and it is economical. Dams are constructed for these purposes.

Bio-Mass:-

   In recent times the cow-dung cakes are used as a fuel to replace the use of wood which leads to the cutting of trees. Since these fuels are from plants and animals they are called as bio-mass.

Wind Energy:-

The Kinetic energy of the wind can be used to do work. This energy is used in the windmills to do some work like, to lift water from well and in water lifting pump. Now this energy is used to generate electricity. This energy is renewable and economical.

Non-Conventional sources of energy

 The technology growth has increased our demand for energy which has led us to invent new forms of sources.

Solar Energy:-

Solar power is an important energy sources of the earth.  All the living power directly or indirectly derive the energy from the solar system that is from the sun.  Solar power is continuous in some part of the world except for the nights.  That means the sunlight is continuous in all part of the year.  The solar energy can be converted into electric energy and heat energy.  Most of the fossil fuels are spend in the developing countries for heating purpose. By using solar energy the pollution can be controlled and the fossil fuel can be saved to other useful thing.

Technology is need to use the solar power to convert into fuel and to be stored.  New type of Batteries are to be invented for storing large amount of energy.

Energy from the sea

Tidal Energy:-
The level of water in the sea rises and falls due to the gravitational pull. These high and low tides give us tidal energy which is harnessed by constructing a dam across the sea. This tidal energy is converted into electrical energy.

Wave energy:-
The kinetic energy by huge waves is used to generate electricity. Technology has led us to invent new devices for this purpose.

Geo Thermal energy

The geological changes have led to the formation of few hot springs. The steam from the spring is trapped and is used to generate electricity. New Zealand and United States of America  are known for this Geo thermal energy.

Nuclear Energy

The process of nuclear fission is used to produce steam and further to generate electricity. The nucleus of a heavy atom is bombarded with low energy neutrons for producing this form of energy.

 We have been gifted by various forms of energies. Exploiting any source of energy disturbs the environment. The non-Renewable energy should be saved and conserved for the welfare of all the life forms on Earth.

Understanding zeroth law of thermodynamics

Let us learn Zeroth Law of Thermodynamics

Let us consider two systems A and B separated from each other by thermally insulated wall (one that conducts no heat), but each being in contact of a third system C through a (diathermic) wall which permits heat to pass. Then the system A will be in thermal equilibrium with system C and similarly system B will also be in thermal equilibrium with system C.
Now if the adiabatic wall between systems A and B is replaced by a diathermic wall, experiments show that no further change occurs in a system A and B indicating thereby the system A was also in thermal equilibrium with B, This important experimental fact leads to the following general conclusion. you can also get help with density of metals . This statement is called the zeroth law of thermodynamics and forms the basis of concept of temperature. All these three systems can be said to possess a property that ensure their being in thermal equilibrium with one another.

Properties of Light

Today's topic is properties of light.

The term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not.

Light is electromagnetic radiation that has properties of waves. The electromagnetic spectrum can be divided into several bands based on the wavelength of the light waves

There are two properties of light

Reflection and Refraction.


Dispersion of Light

The fact that refractive indices differ for each wavelength of light produces an effect called dispersion of light. This can be seen by shining a beam of white light into a triangular prism made of glass. White light entering such a prism will be refracted in the prism by different angles depending on the wavelength of the light.

When light enters a transparent material some of its energy is dissipated as heat energy, and it thus looses some of its intensity. When this absorption of energy occurs selectively for different wavelengths of light, they light that gets transmitted through the material will show only those wavelengths of light that are not absorbed. The transmitted wavelengths will then be seen as color, called the absorption color of the material.

FORMS OF ENERGY

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Energy (is a quantity that can be assigned to every particle, object, and system of objects as a consequence of the state of that particle, object or system of objects. Different forms of energy include kinetic, potential, thermal, gravitational, sound, elastic, light and electromagnetic energy.

Energy transformation in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang, later being "released" (transformed to more active types of energy such as kinetic or radiant energy), when a triggering mechanism is available.

Different forms of energy.

There are different forms of energy, all of which measure the ability of an object or system to do work on another object or system. Listed below are some forms of energy.

Kinetic Energy

Potential energy

Thermal or heat energy

Chemical energy

Electrical energy

Electrochemical Energy

Electromagnetic Energy

Sound Energy

Nuclear Energy