Conservation of Kinetic Energy

Introduction to Conservation of kinetic Energy:

Have you ever observed a ball when thrown vertically upward with certain force? It goes to a certain height and comes back to the ground when it strikes the ground it bounces back in upward direction once again. Do you know what different forms of energy are involved here and what energy conversion is going on in this motion? Before understanding this, let us try to understand what Conservation of Energy is.

For an isolated system, the total amount of energy remains conserved. In other words we can say that energy can neither be created nor destroyed, it can only be changed from one form to the other. Conservation of energy tells that the total amount of energy remains unchanged. However, during a process or activity one form of energy may get changed to the other form, but if you calculate the total amount of energy, it will remain conserved.

Conservation of Energy when Ball Going Up

For an example If a is ball thrown vertically upward. Using our muscle energy, we provide some kinetic energy to ball and ball starts moving with this kinetic energy in upward direction. As the ball goes up its kinetic energy starts converting into potential energy. As a result the kinetic energy of the ball start decreasing and potential energy of the ball starts increasing. Due to decrease in kinetic energy, the velocity of the keeps on decreasing and finally at one point it becomes zero. This is the highest point up to which ball can go. At this point the total kinetic energy of the ball has converted into potential energy.
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Thus at highest point, ball has no kinetic energy and highest potential energy. It is interesting to know that the potential energy as this point is equal to initial kinetic energy of the ball. This is as per the conservation of energy because kinetic energy is converted into potential energy but total amount of energy remains same.

Conservation of Energy when Ball Falls Down

Now ball starts falling down with this potential energy and as it falls down under gravity, its potential energy starts converting into kinetic energy. As a result the potential energy decreases and kinetic energy increases and velocity of the ball goes on increasing. The moment when ball strikes the ground, all its potential energy is converted into kinetic energy and once again due to conservation of energy, this energy is equal to the potential energy at the top as well as to the initial kinetic energy.

Electrical Current Production

Introduction to electrical current production:

Electric current is defined as the migration of electric charge. The electrical current may consist of charged particles that are in motion of any origin; a majority of these comprise electrons. The flow of charged particles forming the electrical current may be in either of the direction or sometimes in both the directions simultaneously.

                                                                Image flow of electron

How is Electrical Current Produced

Current is usually generated by the electromechanical generators which are run by steam obtained from the combustion of fossil fuels or in some cases by the heat that is discharged from the nuclear reactions or production of the current is possible from various other sources such as kinetic energy which is extracted from running water or from wind. Steam turbines produce up to 80% of the electrical current using a large variety of sources. Continuous production of electrical current is required since very large quantities of current cannot be stored that may be required for meeting the large-scale demands of the nation. Generation of electrical current from renewable sources such as hydropower and wind are gaining importance due to concerns with regard to the environment.


Some other Sources of Production of Electrical Current
Burning of fossil fuels such as natural gas, coal, crude oil occurs in the power plants where most of the electric energy is generated. This massive production accounts for the gases emitted into the earth’s atmosphere from the green houses gases. The heat that is produced by burning fuel is generally utilized for the evaporation of huge volumes of water, creating steam that is required by the steam turbine where it is converted into mechanical work. This mechanical work is efficiently converted into electrical current by connecting the drive shaft of the turbine to the mechanical generator.
Using an electrochemical generator for the production of electrical current: An electrochemical generator with a cell that contains an anode compartment and an aqueous solution in motion. The active metallic material loses electrons after being oxidized, which is collected through the anodic electron collector.

                                                     Image of electrochemical generator

Conclusion for Production of Electrical Current

To conclude, electrical current is produced from a variety of sources that range from fossil fuels to wind or water. A change in the magnetic field results in a change in the flux, resulting in the production of electrical current.

Alternating Current Motors

Introduction to Alternating Current Motors:

The electric motor which works under the alternating supply of current is named as the alternating current motor. As the name suggest this motor is driven only by the alternating current and if one give a direct current to the motor then the motor does not work or may get damaged. The alternating current motor consists of two major but the basic parts as, the stator which is generally fixed outside and is stationary but there exists some motor which have the stator fixed within it and the second part is rotor, which is connected both inside and outside the motor. The outside rotor is used to increase the inertia and the cooling of the motor. The outside stator has the coils to which the alternating current is supplied to produce a rotating magnetic field in the coil. The inside rotor is attached to the output shaft of the motor which gives a torque due to the rotating magnetic field. The alternating current motor of a ceiling fan is shown in the fig.1.

                                                   Fig.1 Alternating current motor of ceiling fan

Types of Alternating Current Motors

Without considering the eddy current motors, while going through the alternating current motors, alternating current motors are broadly has two types:

Synchronous motors:  These alternating current motors are the simplest kind of the alternating current motors. They rotate at a frequency which is either exactly same as the supply frequency or is a multiple of the supply frequency. In these motors the magnetic field which is generated on the rotor is either due to the current which is delivered through the slip rings or due to a permanent magnet.
Induction motors: These alternating current motors are also the simple alternating current motors but they rotate at a frequency slightly less than the supply frequency. Thus these motors run slowly. In these motors, the magnetic field which is generated on the rotor is only due to the induced current inside the coil of the motor.


Conclusion on Alternating Current Motors

From the discussion we made on alternating current motors, we conclude the importance of alternating currents and its varied application in day to day life.

Ferromagnetic Domains

Introduction to ferromagnetic domains:
The ferromagnetic substances are those in which each individual atoms or molecules or ions have a non zero magnetic moment as in the paramagnetic substances. When the ferromagnetic substances are placed in an external magnetizing field, they get strongly magnetized in the direction of the field. Ferromagnetism has been explained by Weiss on the basis of domain theory in addition to the usual electron theory.Please express your views of this topic Ferromagnetic Metals by commenting on blog.

Domains in Ferromagnetic Substances

The each atom of a ferromagnetic substance is a tiny magnetic dipole having permanent dipole moment. However in ferromagnetic materials, atoms form a very large number of small effective regions called domains. Each domain has a linear dimension of 1000 A° and contains about 1010 atoms. Within each domain a special interaction called exchange coupling renders dipole moments of all the atoms in a particular direction. Thus each domain is a strong magnet without any external magnetic field. In spite of this, a ferromagnetic substance does not behave as a magnet, because in the absence of the external magnetic field, the magnetic moments of the different domains are randomly oriented so that their resultant magnetic moment in any direction is zero.Is this topic Permanent Magnet Generator for Sale hard for you? Watch out for my coming posts.

When an external magnetic field is applied on the ferromagnetic substance, it gets strongly magnetized. This can be explained as follows:

(i) Displacement of boundaries of the domains, i.e., domain which are oriented in the direction of the applied field increase in size and the domains which are oriented opposite to the field deceases in size.

(ii) Rotation of domain, i.e., the domain rotate till their magnetic moments are aligned in the direction of the applied magnetic filed. This would happen only when the magnetic field applied is very strong.

                                                   Image of the ferromagnetic domains

Conclusion for the Ferromagnetic Domains

From the above discussion we can say that when the domains have aligned along the magnetic field and amalgamated to form a single giant domain. This is how ferromagnetic material gets strongly magnetized in the direction of the applied field. The examples of the ferromagnetic materials are iron, cobalt, nickel and some are the rare earth materials as gadolinium and dysprosium.

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.
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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.