Category: Physics Notes PPT

Machines that convert mechanical energy into electrical energy are called Electric Generators. The electrical energy generated is further transmitted and distributed through power lines for domestic, commercial use. There are two types of generators,

A DC generator is the type of electrical generator that converts mechanical energy into direct current electricity. However, a generator that converts mechanical energy into alternating current electricity is an AC generator.

Do you know why we study generators in their working principle? On this page, we will get to resolve all our queries on the DC generator’s parts,working principle and how we describe it in mathematical terms.

What About DC Generators?

In DC generators, the energy conversion is based on the principle of dynamically induced EMF production. These generators are most suitable for off-grid applications. DC generators supply continuous power to electric storage instruments and power grids (DC). 

()

DC Generator consists of the following parts –

1. Stator – A stator is a set of two magnets placed in such a way that opposite polarity faces each other. The purpose of the stator is to provide a magnetic field in the region where the coil spins.

2. Rotor – A rotor is a cylindrical laminated armature core with slots. 

3. Armature Core – The armature core is cylindrical in shape and has grooves on the outer surface. These slots accommodate armature winding in it. 

4. Armature Winding – These are the insulated conductors placed in the armature core. Because of them, the actual conversion of power takes place.

5. Field Coils – To produce the magnetic field, field coils are placed over the pole core. The field coils of all the poles are connected in series. When current flows through them, adjacent poles acquire opposite polarity. 

6. Yoke – The outer hollow cylindrical structure is known as Yoke. It provides support to main poles and inter poles and gives a low reluctance path for the magnetic flux. 

7. Poles – The main function of the poles is to support the field coils. It increases the cross-sectional area of the magnetic circuit, which results in a uniform spread of magnetic flux. 

8. Pole Shoe – To protect the field coil from falling and to enhance the uniform spread of magnetic flux pole shoe is used. The pole shoe is fixed to Yoke.  

9. Commutator – The commutator is cylindrical in shape. Several wedge-shaped, hard drawn copper segments form a commutator. The functions of a commutator:

Working Principle of a DC Generator

A DC generator operates on the principle of Faraday’s laws of electromagnetic induction. According to Faraday’s law, whenever a conductor is placed in a fluctuating magnetic field (or when a conductor is moved in a magnetic field) an EMF is induced in the conductor. 

()

If the conductor is guided with a closed path, the current will get induced.  The direction of the induced current (given by Fleming’s right-hand rule) changes as the direction of movement of the conductor changes.

For example, consider the case, an armature rotating in clockwise direction and conductor at the left moving in an upward direction. As the armature completes its half rotation the direction of movement of the conductor will get reversed downward. The direction of the current will be alternating. As the connections of armature conductors get reversed, a current reversal takes place. Thus, we get unidirectional current at the terminals.

EMF Equation of a DC Generator

The EMF equation for DC generator is expressed as:

Eg = (PØNZ)/60A

Where,

Eg – Generated EMF across any parallel path

P – Total number of poles in the field

N – Rotational speed of armature(rpm)

Z – Total number of armature conductors in the field.

Ø- Magnetic flux produced per pole.

A – number of parallel paths in the armature.

Losses in DC Generators

While converting the mechanical energy into electrical energy, there are losses of energy i.e. whole input isn’t converted into output. These losses are classified into mainly three types:

Copper Loss- These losses occur while current flows through windings and are of three types: armature copper loss, field copper winding loss and losses because of brush resistances.

Iron Losses- Due to the induction of current in the armature, eddy current losses and hysteresis loss occur. These losses are also called Core losses or Magnetic losses.

Mechanical Losses- Losses which occur because of friction between the parts of the generator are called mechanical losses.

Types of DC Generators

The three types of self-excited DC generators are:

Applications of DC Generators

Applications of DC generators are as follows:

1. The separately excited type DC generator is used for power and lighting purposes using the field regulators.

2. The series DC generator is used in arc lamps for stable current generator, lighting and booster.

3. Level compound DC generators are used to supply power to hostels, offices, lodges.

4. Compound DC generators are used for supplying power to DC welding machines.

5. A DC generator is used to compensate for the voltage drop in the feeders.

Orbital velocity refers to the velocity required by satellites (natural or artificial) to remain in their orbits. The orbit or the orbital pathway, whether elliptical or circular, displays a balance between the inertia of the satellite which makes it move in a straight line with the gravity of the planet which pulls the satellite closer to the planet. Now, this orbital velocity depends on the distance between the center of the planet and the satellite revolving around it.

 

This velocity applies to planets revolving around the sun as much as it applies to natural or artificial satellites revolving around a planet. The orbital velocity would be higher if the center of attraction is a more massive body at a particular altitude, for example, if a satellite is close to the surface of the earth, and there is not much air resistance, the orbital velocity can be as high as 8 km per second. On the other hand, the further the satellite is from the center of the body of attraction, the weaker will be the force of gravitation due to decreased centripetal force, and therefore, less velocity will be utilized by the satellite to remain in the orbit.

 

The Formula for Orbital Velocity

The orbital velocity equation is given by:

[Rightarrow v = sqrt{frac{GM}{r}}]

Where,

R is the radius of the orbit,

M is the mass of the central body of attraction,

G is the gravitational constant.

The orbital velocity can be calculated for any satellite and the consequent planet if the mass and radii are known.

 

Orbital Velocity Formula Derivation

The following steps can be followed to derive an expression for the orbital velocity of a satellite revolving in an orbit.

For orbital speed derivation, both the gravitational force and centripetal force are very important. Gravitational force (Fg) is the force exerted by the body at the center to keep the satellite in its orbit. Centripetal force (Fc) justifies the existence of circular motion.

 

For this derivation, we will assume a uniform circular motion. Therefore, for an object in orbit, both these forces will be equal.

[Rightarrow Fg = Fc – – – – 1]

Now, as we know gravitational force depends on the masses of both objects and it’s formula is:

[Rightarrow Fg = frac{GMm}{r^{2}}]

Where,

G is the gravitational constant, M is the mass of the central body, and m is the mass of the revolving body, and r is the distance between the two bodies.

Also, the centripetal force is related to mass and acceleration, and the formula for which is given by:

[Rightarrow Fc = frac{mv^{2}}{r}]

Where,

m is the mass of the satellite in orbit, v is the speed, r is the radius of the orbit.

Now, putting both of these equations in (1),

We get,

[Rightarrow Fg = Fc]

[Rightarrow frac{mv^{2}}{r}]

[Rightarrow frac{GM}{r} = v^{2}]

And henceforth,

[Rightarrow  v = pm sqrt{frac{GM}{r}}]

Therefore, orbital velocity derivation is proved.

 

Difference Between Orbital Velocity and Escape Velocity

Escape velocity is the base speed required for a free, non-propelled object to escape from the gravitational impact of a huge center body, that is, to move an unlimited distance from it. This velocity is a component of the mass of the body and separation to the focal point of mass of the body.

 

To find the difference between escape velocity and orbital velocity, let us consider an ideal situation where there is no air resistance and all the bodies are point masses.

 

An orbital speed would be any speed that retains the point mass into a curved or an elliptical direction. It is any velocity that is less than the escape velocity. There are limitlessly many orbital velocities.

 

Escape speed on the other hand is the speed that would place the point mass in a parabolic direction. For any point in space in a two-body framework, there is actually one escape speed. This, numerically, compares to the way that all parabolas have the very same mathematical shape- they just vary in scale. In the interim, there are endlessly numerous curved or elliptical shapes.

 

Escape velocity is the velocity at which the kinetic energy of the object approaches the base of all likely energy out to infinity, which means the object could get away from the gravity of a body completely. Orbital velocity, on the other hand, depends on the precise orbital trajectory; however, for a roundabout circle, it gets away from the velocity at that separation isolated by the square root of 2. Therefore, the object is not getting away into infinity; it is simply falling in a circular motion around the center body.

 

The velocity required by a satellite to be in its home orbits is called orbital velocity. So now what about escape velocity. It has got the absolute meaning just like the name escape! Yes, it is the velocity required for releasing down from its primary place and to reach the infinite distance. It can also be called an ideal speed. This is because here we have to ignore the friction offered by the atmosphere. And a close relationship with the mass of a primary body is, the escape velocity increases with an increase in the mass of the primary body. And how it decreases is by the distance from the primary body.

The relation between orbital velocity and escape velocity is given by 

[V_{e} = 2V_{0}]

Where [V_{e}] is escape velocity and [V_{0}]is orbital velocity.

 

How Escape Velocity Works!

We all know about gravitational force. To reach space, the satellite should be able to overcome this pull. And thus it needs to have a specific velocity called escape velocity to reach the distance it intends to. Lower velocity is needed if the distance from the primary body; in our case, it is the earth, higher the distance. So that is why the communication satellites orbiting the earth don’t consume any energy. Because they are at a distance of miles away from the earth. However, commercial aircraft require much energy to stay in the atmosphere for having control over the gravitational pull. 

 

For a rotating body, its escape velocity depends upon the direction it is going. However, apart from theoretical considerations, there is so much we have to decide upon the practical considerations. For example, in real life, it is not that easy to achieve escape velocity instantly. Since the acceleration is already implied and with the hypersonic speeds, there are chances of getting burned as a result of aerodynamic heating. And taking into consideration an elliptical orbit, for getting into the escape velocity for the body the required speed will always vary. Also when the body is closest towards the central body it will be at the greatest at the periapsis.

 

The Black Hole’s Escape Velocity

We already have a brief idea about black holes. For anything that is near the black hole is taken inside. And the escape velocity for something that enters a black hole is nearly more than the speed of the light.

< span> 

However, there are black holes that are formed at the center of galaxies ejecting the matter absorbed in the speed of the light. They are called quasars.

 

Conclusion

offers free downloads of Orbital velocity in PDF format. In addition offers solved examples, step by step derivations, self study materials such as mock question papers, worksheets  and previous year solved question papers.

Class 11 students are expected to know the exact spherometer experiment procedure. You will need to determine the radius of curvature of given spherical surfaces using this device. However, before proceeding to learn about the process of doing the same, one should understand spherometers in detail.

 

What is a Spherometer?

A spherometer is one of the vital scientific devices that measure the radius of curvature for any spherical surface precisely. Initially, opticians used these devices to create and determine powered lenses. 

 

We come across various instruments that are used in a lab for the measurements of different things but when we have to measure the radius of curvature of either a sphere or a curved surface with its precise measurements, then we use an instrument called a spherometer. Now if you look back at the history of the spiral meter we see that it was invented by Robert-Aglaé Cauchoix, his profession was that of an optician in the year 1810. Robert mainly manufactured the spherometer for the use of opticians in grinding lenses. Other than using it for grinding lenses or in the physics lab, sphere meters are used by astronomers for grinding lenses and curved mirrors. Accordingly, spherometers can have various other uses as well.

Now before we go ahead with the understanding and definition of the spherometer we will see the working principle of the device. The working principle of a spherometer is based on a micrometer screw which is used for measuring a small thickness of flat material such as gas or can be used for measuring the radius of curvature of a spherical surface.

 

Normally a spherometer can be described as a device consisting of a base of a  circle of three of the leg, central leg and a reading device. The Circle of three or three legs is also known as the radius of the base Circle and the land along with it is known as the radius of the base circle, the outer legs which are given can be adjusted accordingly depending on the inner holes, this procedure is mainly done to accommodate smaller surfaces. The central leg of the spherometer can be moved in an upward and downward direction accordingly, this can be called a flexible method of drawing lines or using it with any other measurements. For taking the measurements any device on the reading device should be moved accordingly.

 

How to use a Spherometer?

A spherometer is a very common device in labs, opticians, and other physics-related settings but the main thing that is necessary is to know and understand how to use a spherometer. There is a certain set of procedures that are included while using a speedometer: 

• After holding the instrument, it is first placed on the perfect plane surface in a manner that the middle foot is screwed down slowly till it touches the surface below. After the middle foot touches the surface, the instrument turns around on the middle foot as the center, now the center has a point from which we can equally draw shapes accordingly or measure.

• After the surface is made the spherometer is then carefully removed from the surface to take the readings from the micrometer screw. The instrument should show the reading 0-0 in normal cases, this reading comes when the instrument is working fine, any other reading might lead to errors. If there is any sort of slight error in the instrument it could be either a negative or positive error.

• Now, when we measure the instruments reading, we take the instrument of the plane and let the middle foot back.

• When we are measuring we come across a reading below the zero line so if we see that reading it should be added to the zero error. If the reading above the zero lines is indicated then the reading should be subtracted from the zero error in order to make it balanced.

• To measure the length between the two legs, the instrument should be placed on the plane surface or a playing card while using a meter scale so that equal length is measured
  

To measure the radius of curvature using a spherometer, one must know its various parts. The device has a screw with a moving nut in the middle of a frame with three small legs to support it upright. The table legs, along with the screw, have tapered points to help them rest on a specific surface.

 

Additionally, a spherometer’s least count can differ from one device to another and each time that we may use it to determine the radius of curvature, we still need to calculate this acquired count again. 

 

Define Spherometer Least Count

The smallest value that a spherometer can measure is known as its least count. The formula for determining the least count is as follows – 

 

Least count = Pitch/Number of divisions on its head scale

 

Typically, the least count is always 0.01 mm. 

 

Experiment to Find Radius of Curvature using Spherometer

Now that you know some of this measuring device’s basics, let us learn more about this experiment in general.

1. Aim

To find the radius of curvature using spherometer of a spherical surface

2. Apparatus Necessary

Plane mirror, spherometer and convex surface

3. Table Format for Noting Experiment Data

 

Complete Procedure for the Experiment

• Step 1: Raise the central screw of this device and use a paper to track the position of a spherometer’s three legs. Join these three points on the paper and mark them A,B and C. 

• Step 2: Measure the minute distance between the three points. Note the three distances (AB, BC and AC) on a sheet of paper.

• Step 3: Determine the value of one pitch (or one vertical division).

• Step 4: Record the least count of your spherometer.

• Step 5: Raise the screw upwards to prepare for the measurement.

• Step 6: Place this spherometer on the spherical surface in such a manner that all three legs are resting on the object.

• Step 7: Start turning the screw so that it barely touches this convex surface. 

• Step 8: Take the reading of both the vertical scale and the disc scale in such a position. This will act as your reference point.

• Step 9: Now place this spherometer on a plane glass slab.

• Step 10: Move the screw downwards and count the number of complete rotations for the disc (n1).

• Step 11: Continue moving until the screw tip touches the glass slab. 

• Step 12: Note the reading (b) on this circular scale in relation to its vertical scale.

• Step 13: Note the circular divisions for its last incomplete rotation.

• Step 14: Complete steps 6 to 13, thrice. Note readings each time in the tabular format mentioned above.

Observations

Mean value or l = [frac {AB + BC + AC}{3}]

h = [frac {h_1 + h_2 + h_3}{3}]mm (Convert into cm)

 

Calculating Radius of Curvature of Convex Lens using Spherometer Readings

Radius R = [frac {I^2}{6h}] +
[frac {h}{2}] cm

 

’s interactive classes can help you understand more about spherometer readings, the radius of curvature and more. Experienced teachers are at your disposal whenever you need your doubts cleared.  It helps a child strengthen his or her basic concepts when understood in a processed and elaborate manner and uses point-to-point examples and explanations from the given terms so that it becomes easier to understand complex terms as well.  you can also download our app for better access to these study materials and online interactive sessions.

Electric Current flows either in one Direction or keeps changing its Directions periodically. Hence, there are two ways of Current flow, namely; Alternating Current (AC) and Direct Current (DC). The major difference between AC and DC is that Current electricity flows gradually in one Direction in the Direct Current (DC). However, Current continuously varies its Direction from forward to backward and vice versa. Learn more about the points that distinguish between AC and DC. 

What is an AC Current?

The term AC refers to Alternating Current in Physics, which is highly preferred electric power for office, household equipment, and more. The critical difference between Alternating Current and Direct Current lies in the Direction in which electric charges flow. In AC, electrons continuously change their Directions from forward to backward periodically.

The curve of an Alternating Current when drawn on a graph represents the sine waveform. The curved lines denote electric cycles that are measured per second. As compared to DC Current, it’s easy to generate and transport AC across large distances. Hence, Alternating Current is widely used in buildings, powerhouses, and more. 

What is a DC Current?

DC refers to Direct Current in which there is no change in the Direction of Current flow. Hence, the major difference between AC and DC Current is the electric current flows only in One Direction in a stable voltage in DC Current. One of the major uses of DC is to charge batteries and supply power for electrical devices. In the DC circuit, electrons emerge from the negative side and move towards the positive side. The basic source of DC is produced by photovoltaic cells, batteries, or electrochemical cells.  

The above image shows that Direct Current flows in one direction. The graph shows the proportionality between the magnitude of DC and time.

Anything that uses an AC adapter while plugging into a wall or that runs on a battery depends on Direct Current. Some of the examples of DC include flashlights, mobile phone batteries, electric vehicles, and more. By going through the difference between AC Current and DC Current, it’s easy to understand why AC is most referred to across several applications. 

How Alternating Current is Converted into Direct Current?

There are several cases when there is a necessity to convert AC into DC. It’s because of the AC and DC difference that Direct Current is less preferred over long distances. To convert AC into DC, a power supply that consists of a transformer is required. Later it gets converted into Direct Current with the help of a rectifier. The conversion of AC into DC is beneficial to prevent the flow of Current from reversing. A filter used eradicated the Current pulsations in the rectifier output.

To sum up, the points of difference between AC and DC include:

Differentiate Between AC and DC Current 

Ohm’s Law

Ohm’s Law frames that the voltage across an electric conductor is Directly proportional to the Current flowing via it (provided all physical necessities and temperature remain constant). Ohm’s Law is useful only when the given temperature and the other physical factors stay constant. In certain components, expanding the Current raises the temperature. For Example-  the filament of a light bulb, in which the temperature increases as the Current is increased. Ohm’s Law cannot be applied to such conditions because the Current is a variable here. The lightbulb filament breaks Ohm’s Law.

Faraday’s Law

Faraday’s Law or the Law of electromagnetic induction is the essential Law of electromagnetism, which allows to indicate how a magnetic field would interact with an electric circuit to generate an emf (electromotive force) which is also called electromagnetic induction.

Faraday’s Laws of Electromagnetic Induction consists of 2 Laws. They are-

1. Faraday’s First Law of Electromagnetic Induction- Faraday’s First Law of Electromagnetic Induction states that an emf (electromotive force) is caused in the coil when the magnetic flux across the coil varies with time.

2. Faraday’s Second Law of Electromagnetic Induction- Faraday’s Second Law of electromagnetic induction remarks that the induced emf (electromotive force) in a coil is equivalent to the rate of change of the flux linkage.

Conduction

Conduction is the method of transferring heat within a body or from one body to another caused by the heat transfer by molecules vibrating at their mean positions. The bodies involved in the heat transfer must be in contact with one another. When heat is transferred from one location to another, there is no actual movement of matter.

Conduction is most frequent in solids, where molecules are kept together by intermolecular forces of attraction, causing them to only vibrate about their mean locations as they receive heat energy and hence pass it on to the surrounding molecules via vibrations.

Convection

Convection is a heat transport method that occurs mostly in liquids and gases. Heat transfer occurs in this mechanism when the substance is moved from one location within the body to another. Eg. It is often witnessed bubbles and currents arise in boiling water. (Fig 1)

This is an excellent illustration of the convection process. The hot water at the bottom gets lighter and rises, causing the colder, denser water at the top to descend and heat up.

Radiation

Another method of heat transport is radiation. It works without the use of a medium and can even transfer heat in a vacuum. Electromagnetic waves are used in this way to transfer heat from one location to another. Radiation is how the sun’s heat and light reach our planet in our solar system.

Radiation is, in fact, the most powerful means of heat transport. We feel warm without touching the burning wood when we sit near a fire in the winter. Only radiation makes this possible.

Differences

One of the primary differences between kW (known as kilowatt) and kVA (known as kilovolt-ampere) is the power factor. The unit of KVa is used to represent apparent power and KW is used to represent the real power of an electrical system. Both of their usages differ in electrical circuits because of the difference between AC and DC circuits. When we consider a DC circuit, the kW and kVA are equal because the current does not get out of a phase. But, when we consider an AC circuit, we could find out several differences.

Generally, the kW rating is the power which is the resulting output a generator can supply which is based on the horsepower of an engine.  The kW is figured out by horsepower rating of the times of the engine.  If kW is the amount of force we can work with, kVA explains the amount that is being used in the framework. Eg: When we say that if we have a 500 horsepower engine it has a kW rating of something around 373. The kilovolt-amperes which are denoted by kVA are the generator end capacity. In this topic, we have learned the difference between kilowatt and kVA. Let us dive more into it.

Difference Between kVA & kW

Kilowatt, which is denoted by kW, is the unit that we have learned in school and how electricity at home is rated and the unit can be seen in our electricity bill. 

So, the question arises what’s the difference between kVA & kW? How do we convert both of them?

kVA is said to be a measure of apparent power. It tells us the total amount of power that is used in a system. In a 100% efficient system kW = kVA. However, the electrical systems are never 100% efficient, and therefore, not all of the power of the system which is apparent is being used for useful work output. 

The kW that we are aware of is the amount of power that is converted into a useful output. The kW is said to be therefore called actual power or working power. We can easily convert between kVA and kW if we know the efficiency of the electrical system. The efficiency in the Electrical system is expressed as a power factor between 0 and 1.

The kW is the amount of ‘actual power’ an electrical system has. This will show how much power is being converted into useful work that is basically for working output.

To convert kW to kVA we first need to know the efficiency or power factor of the system. The factor which is of Power is denoted by pf and is measured on a scale from 0 to 1.

The kW to kVA conversion formula is –

kW = kVA × PF

Where kW is the unit estimating real power,

kVA is the unit estimating apparent power,

PF is the Power Factor.

In the kW to kVA conversion formula kW is directly proportional to kVA, which implies that-

When kW increases, kVA will increase.

When kW decreases, kVA will decrease.

When kVA decreases, kW will decrease.

When kVA increases, kW will increase.

On average we can easily say that a generator has a power factor of 0.8.

The formula used for converting kW to kVA is: kW / pf = kVA e.g. 200 kW / 0.8 pf = 250 kVA

The formula which is for converting kVA to kW is: kVA x pf = kW e.g. 250 kVA x 0.8 pf = 200 kW

These calculations can help us in various industries. Eg: If we want to purchase generators from our local sales, the engineer will be able to help us identify the most suitable equipment for our project. They will take the time to get to know about our job and discuss exactly what we will be powering and for how long. From there they can advise on the generator which is most suitable for us.

kVA to kW Conversion

These two units of power are significant to solve many problems in physics. kVA to kW formula conversion is: kVA = kW / PF

Difference Between kW & kVA Conversion

To convert kW to kVA the formula used is:

kW=kVA × PF

Did You Know?

• A very small fraction of kVA is accessible to do any work, the rest fraction is considered in the current.

• kW represents the actual power that does the valid work.

• In the DC circuit, the kW and kVA are both equal because the current does not go out of the phase. While in the  AC circuits, many differences can be found.