[Physics Class Notes] on Natural Sources of Energy Pdf for Exam

Energy is one of the most important entities in our universe. We perform many day to day activities. Think, what causes humans to do all the daily activities? This capacity or ability of a body or system to do work is referred to as energy. 

Energy is thus a qualitative property that needs to be transferred to another object in order to make it work or function. Energy can neither be created nor destroyed. It can only be transferred or converted from one form to another. As energy exists in multiple forms, it is hard to find a single elaborate definition of it. Energy can be chemical, thermal, mechanical, electrical, nuclear and light etc. 

The SI unit of energy is Joule (J), which is defined as the energy spent in making an object move through a distance of 1 m, against a supplied force of 1 newton. We will now discuss a few sources of energy in this article below.

Types of Natural Sources of Energy

Energy sources are of two types:

  1. Renewable energy sources

  2. Non-renewable sources

Renewable Sources of Energy

The sources of energy present on the earth that can get replenished, or recharged without getting exhausted (running out) are called renewable sources of energy. Renewable energy sources are available on a daily or seasonal basis. Renewable sources are clean and do not cause any pollution to the environment. For example: sun, wind and water etc.

The sun is a very essential source of renewable energy in our life. Our sun is a star i.e. its light is internally produced, it does not reflect the light of any other star or body. It is the basic source of heat and light for the entire living world and the source of energy for all ecosystems. Its thermal heat can be used for passively heating buildings and water. Its natural light (daylight) contributes immensely to the reduction of artificial light needed to light our buildings. It is useful for plants to grow. Sun can provide electrical energy with the help of photovoltaic cells (PV Cells), which are made up of silicon or any other material that transforms sunlight into electricity. Solar panels absorb the sunlight and store it in a solar battery. Solar panels convert solar energy into usable electricity by the photovoltaic effect. Solar energy is also used as solar thermal energy.

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Wind energy is an environment friendly and abundantly available source of energy.  Windmills are used to harness the wind potential. Wind rotates the turbine’s blades, which feeds an electric generator and produces electricity. The turbine makes use of kinetic energy of wind and converts it into mechanical energy. The generator can convert mechanical energy into electricity. Mechanical energy can also be used directly for specific tasks such as pumping water etc.

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Water or hydel energy is the energy derived from the flowing water. Electricity produced by the flow of water using dams is called hydroelectricity. In this process, a hydel dam captures energy from the moving water of the river. This water is made to fall from a great height. The falling water rotates the turbine, which feeds the generator. The dam operators control the flow of water and the amount of electricity produced.

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Non-Renewable Sources of Energy

Non-renewable energy sources are those which are present in a limited quantity. They are exhaustible, and will run out if not used judiciously. These sources cause pollution to the environment because carbon is the main element present in fossil fuels such as coal and petroleum. Most sources of non-renewable energy are fossil fuels. Fossil fuels were created as the remains of terrestrial and marine flora and fauna that decayed millions of years ago and got buried in layers under huge amounts of pressure and heat. Most fossil fuels are burnt to produce energy and electricity. Coal is also a fossil fuel.

Fossil fuels are a valuable source of energy. They can also be stored, piped, or shipped anywhere in the world.

Coal is a black coloured rock-like fuel. We burn coal to get energy. Coal is widely used as a domestic fuel to make food. When coal is burnt, it releases harmful smoke. Coal is essentially formed as a result of decayed vegetation. There are four stages in the formation of coal- peat, lignite, bituminous and anthracite. Coal mainly contains carbon, hydrogen and oxygen. 

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Petroleum is a liquid fossil fuel composed of a variety of hydrocarbons. It is a very useful energy source. However, the petroleum that is drilled out from oil wells is crude oil. It has to be refined through a process called fractional distillation, where different hydrocarbons separate to form different fractions. Petrol, kerosene, paraffin, diesel are some of its fractions.  Petrol is used as a fuel in vehicles. Petroleum and its products are used not just for transport but also to manufacture many different products such as plastics, tyres and synthetic materials such as polyester. It is a reliable & portable source of energy. However, the burning of both coal and petroleum is harmful to the environment.

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[Physics Class Notes] on Noise Pdf for Exam

We know that sound is a form of energy. Sound is a mechanical wave and the study of sound starts with the properties of sound waves and the types of sound waves. Basically, the sound is generated in the form of a wave or vibration. Human ears are extremely sensitive to sound waves ranging from 20Hz to 20KHz, known as audible sound range. There are many categories of acoustical sound such as pleasant sound, unpleasant sound, music, noise, soft, loud, etc. 

Now, noise is also a type of sound, it is really important to distinguish between what we mean by noise and what is sound. Noise is a type of sound and it can be explained or defined as a type of sound that can be unpleasant, unwanted, annoying or too loud for human ears. Noise acoustics will help us in understanding what is noise and how it can be reduced. In this article, we will discuss noise and noise acoustics by understanding how noise is produced and different types of noises.

Noise Acoustics

We know that human ears are highly sensitive and excellent at recognizing noise. Generally, noise is a kind of unpleasant and annoying tone of sound that causes mild to major discomfort or sometimes it may lead to irritation. These noise sound vibrations are capable of piercing through the ground noise that accompanies our lives. When it comes to the measuring of the various sorts of noise, we would like to duplicate how the human ear identifies and recognizes any kind of noise to urge an accurate interpretation of its impact. 

Thus, generally, in noise acoustics, we use something called the A-weighted frequency, which is considered to be much more sensitive between the frequencies 500 Hz and 6 kHz range. Depending on these frequency range there are four different types of noises, as listed below:

  • Continuous noise

  • Intermittent noise

  • Impulsive noise

  • Low-frequency noise

Let’s discuss the four sorts of noise one by one as follows:

1. Continuous Noise:

According to the name of the type of noise, we can say it is a kind of noise that is produced continuously. The specimens used or any sample of continuous noise are all mainly caused due to the machines that run continuously with no breaks in between, just like while riding a car we hear the sound of functioning parts especially such as the sound of an engine. The main source of continuous noise could be the production factories, we have seen that in factories large machinery produce continuous noise such that barely we can hear anything else.

2. Intermittent Noise:

  • The intermittent noises are such sound frequencies that are not produced continuously. At the same time, the intermittent noises are produced continuously but with particular intermediate breaks.

  • The best day to day illustration and example of the intermittent noises are the drilling machines, which we would have seen during the destruction or construction of any kind of building. The drilling machines are used to drill the ground and these machines reproduce unbearable sound.

  • Another best and relative example of intermittent noise is drilling machines employed by a carpenter or the dentist.

3. Impulsive Noise:

  • The impulsive noise is a kind of noise characterized by a background level of audible range up to 40dB in less than a half-second with a duration of 1 second.

  • Impulsive noises mainly include almost all unwanted, unpleasant and instantaneous sharp sounds.

  • The best examples of impulsive noises are bomb explosions that are terrifying and unbearable, the perimeter of weapons, and so on.

4. Low-Frequency Noise:

  • The low-frequency noises are generally produced from the items available in our surroundings in our everyday life. The low-frequency noise is one of the complicated types of noise to scale back, and even if it is measured in a silent room still it would register sound levels around only 30-40 decibels.

  • The low-frequency noise can be noticed in an office setting, this noise might have been produced from heating or ventilation. In domestic cases, it will arise from the ticking on a timepiece or wall clock. Usually, we can not even recognize these sorts of noises unless we direct our attention towards them.

So, these are the various types of noises and what is the meaning of noise physics. In analogue electronics and network theory, the word noise refers to those random, unpredictable, and undesirable signals, or mutations in signals, that cover the specified and desired information and the content. At the same time noise in the radio signal transmission seems to be as a static wave and in television signals as snow. depending on the complexity levels, the noises are subdivided into white noise and pink noise. Let us have a look at these two one-by-ones.

A. White Noise:

The white noise may be referred to as a complex signal or sound wave that incorporates the whole range of audible frequencies, all of which possess equal intensity. White noise is identical to white light, which contains merely equal intensities of all frequencies of light present in nature. A good approximation to white noise is that the static waves found in between the radio stations on the FM band.

B. Pink Noise:

The pink noise includes all the frequencies of the audible spectrum but with an intensity that will considerably decrease with increases in frequency at a rate of three decibels per octave. This decrease in frequency roughly corresponds there to acoustic (non-electronic) musical instruments or ensembles. Thus, the pink noise has been used in checking the listening rooms and particularly for auditoriums for his or her acoustic characteristics and parameters, such as reverberation time, sound-absorbing, and undesirable resonance behaviour which are the most important parameters in noise acoustics. It can also be used in audio equalizers to supply a linear intensity versus frequency response within the available listening environment.

Any kind of noise can be eliminated by providing the rooms with sound proof walls or by sound blocking. These days acousticcurtains are constructing the building by keeping the acoustic soundproofing walls for the buildings and auditoriums.

Did You Know?

1. The Maximum Loudest Sound the Earth Has Ever Produced: 

The loudest natural sound or the noise on Earth are produced by erupting volcanoes. In the year 1883, the volcano eruption that took place on Krakatoa is considered to be the loudest noise that had bee
n produced on Earth. 

2. The Noisiest City in the World: 

According to the recent survey and the research conducted by City Quiet, the top three noisiest cities in the entire world are Mumbai (India), Kolkata (India) and Cairo (Egypt). These cities are also subjected to maximum noise pollution due to the same reason.

3. The Loudest Animal on Earth: 

Even though we have heard that the call of a blue whale reaches 188 decibels, which is even louder than a jet engine or any grenade explosion, yet the loudest animal on Earth is the sperm whale whose communicative signals have been measured about up to 230 dB.

4. We have to consider an important fact that the root and main source of noise in urban environments: According to the survey and research of a European Environment Agency (EEA) briefing ‘Managing exposure to noise in Europe’, the transport sector is a major reason for noise pollution. Road traffic is the predominant noise source affecting approximately around 100 million people in the 33 member countries of the EEA.

[Physics Class Notes] on Optical Density Pdf for Exam

Basically, the physical density would be the ratio of mass to the volume, and optical density measures the speed of light while passing through an optically dense medium. 

 

The optical density is a property of a transparent material that measures the speed of the light through the material. The extent to which any optically dense medium bends transmitted light rays towards or away from the normal is called the optical density.  

 

The light passing via an optically dense medium bends towards the normal and if the same light passes via any rarer medium such as air, it bends away from the normal.

 

Optical Density

Now, let us understand the phenomenon of optical density and its effect on the light passing via a medium by comparing the two media.

 

Consider two mediums: glass and air. When a beam of light passes from air to glass. The speed of the light decreases in the glass. It tells us that the glass is optically denser than air.

 

Which means,

The velocity of light in glass (denser medium) is less than the velocity of it in rarer medium (air).

 

If the same light passes from glass to air. The speed of light increases. 

Which means,

The velocity of light in the air (rarer medium) is less than the velocity of it in glass (denser medium).

 

What is Transmittance?

The transmittance of a medium or a material is defined as the constituent of the light that moves via the other side of the medium or the ratio of the light energy falling on it to the light transmitted through it. When light passes through any medium, it can be transmitted, reflected, or absorbed.

 

The transmittance of the light can be defined as the ratio of the intensity of incident light (Io) to the amount of intensity (Ia)  passing through the medium. It is denoted by T.

 

Where,

 

The transmittance has no unit.

The ratio of radiant flux transmitted by the material (Φt) to the radiant flux (Φi) received by that surface is known as the Transmittance (T).

 

Transmittance Formula

T = Φ t /  Φ i is the transmittance of the material.

 

Here, the radiant flux is the radiant energy emitted, reflected, transmitted, or received, per unit time. Its unit is Watt and the SI unit is Joule per second (J/s)

 

Optical Density formula

An optical density is defined as an equation given by, 

Optical density (O.D.) =  log₁₀ Io / It

 

The optical density of any medium is defined as the logarithmic ratio of the intensity of incident light (Io) to the intensity of the transmitted light (It) passing through that medium. 

The O.D value for absorbance can be computed by the formula given by,

O.D. Value

Absorbance (A)  = log₁₀ (100) / (%T)

 

Where, Io is the intensity of visible light incident upon a small area of the film and It, the intensity of light transmitted by that region. T% is the percentage of transmission.

 

The Relation Between Optical Density and Absorbance

The optical density and absorbance both measure the absorption of light when that light passes through an optical medium however they both are not the same.

 

Optical density measures the ability of an object to slow or delay the transmission of light. It measures the speed of light via a substance which is affected mainly by the wavelength of the given light wave.

 

Absorbance, in a wave motion, is the transfer of the energy of a wave to matter as the wave passes via it. If there is only a fragmental absorption of energy, the medium is said to be lucid to that particular radiation, but, if all the energy is lost, the medium is said to be opaque. Therefore, absorption of light occurs more in an optically dense medium.

 

Absorption Unit

The absorption unit is basically used in ultraviolet-visible spectroscopy where AU is a dimensionless quantity denoted by AU. 

Absorption of any material is taken as A given by,

(A)  = log₁₀ (100) / (%T)”

Where Φ t is the radiant flux transmitted by that material and, Φ i is the radiant flux received by that material. T is the transmittance.

 

How does Concentration Influence Optical Density?

Since optical density can influence the speed of light due to optical absorption, it is quite evident that the concentration can also influence the optical density of the matter. If the optical density of the material is higher in value then it will decrease the speed of light and this causes the light to change its motion. Due to the slower speed of light, it will bend. Optical density is influenced by the concentration of light due to optical absorption. With increased concentration, the optical density of the matter will also increase.

The Significance of Optical Density

The concept of optical density helps the students to understand the speed of light transmission. The concept of optical density helps students to understand why the speed of light decreases when passing through a particular substance and the importance of the wavelength of the light transmitted through the medium. This is an important concept of physics that explains a lot of phenomena involving light emission and transmission.

Difference between Optical Density and Absorbance

Optical density measures the degree of the angle to which a particular medium slows down the speed of the transmitted light. Absorbance measures the capacity of a particular object or a medium to absorb the transmitted light that is of a specific wavelength. The concept of optical density takes both the phenomenon into account, that is the absorption of the light of a specific wavelength and the amount of light that is scattering.

The Best Way to Understand the Concept of Optical Density

The best way to understand the concept of physics is to take practical examples and analyse them on the basis of the knowledge of a particular topic. The concept of optical density explains what are the influential factors that can change the course of the lig
ht and can even lower the speed of the transmitted light. There are some practical examples that we can find around ourselves. The students can consider these items to understand the concepts of physics. Optical density takes the absorption of light by a particular medium, the scattering of the lights of different wavelengths, and the refractive index into account.

All these associated concepts can be understood by the students if they are provided with proper examples. Different types of objects can influence the speed of the light and its motion depending on the mass or the optical density, and the power of absorption. The concept can also help the students to establish relationships between the optical density, refractive index, and the speed of the light. The more the refractive index is, the more will be the optical density of a particular matter and will affect the speed of the light inversely.

The students can also refer to various reference books and textbooks prescribed by CBSE to understand various concepts of Physics. The subject-specific NCERT books are available on the website of for free. The NCERT books of physics, chemistry and biology are available on the website along with the other revision notes that can help the students to memorize the important facts that they have already learned.

How does the Intensity of a Particular Medium Influence the Speed of Light?

When light passes through a denser medium it has to face more particles and due to the absorption of the different wavelengths of the light, the speed of the light decreases. For example, when light passes through the medium of air, the frequency of the wavelength and the speed will not be affected by the medium. But when light passes through the medium of water or glass, the speed of the light decreases gradually.

[Physics Class Notes] on Parity Pdf for Exam

In Physics, parity is a feature that is significant in describing a physical system using quantum mechanics. It usually has to do with the symmetry of the wave function that represents a system of fundamental particles. A parity transformation is a type of mirror image that substitutes such a system. In mathematical terms, the system’s spatial coordinates are inverted through the origin point; that is, the coordinates x, y, and z are substituted with x, y, and z. In general, a system is said to have even parity if it is identical to the original system following a parity transformation. Its parity is odd if the final formulation is the inverse of the original. Physical observables that are dependent on the square of the wave function are unaffected by parity. The overall parity of a complex system is the product of the parties of its constituents.

Conservation of Parity

A Physics principle says that two mirror images of each other, such as left-spinning and right-spinning particles, should act the same. The idea does not apply to subatomic particle interactions that are weak.

Fundamental Particles Sign

In the study of basic particles, there have been some remarkable breakthroughs in recent years. One of the outcomes has been the appearance of a new language and a huge number of new symbols in scientific writing. Specific types of particles are designated by symbols such as,, and. Others have been used to characterize only phenomenological behaviour (e.g.,). Various authors have given different names to the same particle or assigned different meanings to the same symbol. The meaning of a sign can sometimes alter throughout time. To offer an example, the Greek letter was originally employed to denote a heavy meson that stopped in the emulsion and then decayed, resulting in a single ionising particle. Later, the Latin letter K was substituted for the Greek letter as a code for the above-mentioned phenomenological description.

While the letter took on a more concrete physical meaning: a hefty meson that decays into one charged and two neutral particles. The letter K is also often used to represent any charged particle that is heavier than a -meson but lighter than a proton and whose method of disintegration is unclear. Another example is the neutral particle with a mass of roughly 1,000 m e that decays into two -mesons, which has been given numerous names such as v0, V 20, and V 40, although some authors have used the letter V 20 to identify any V0-particle other than the so-called V 10. Parity is also known as Multiplicative Quantum Number. Parity is a useful concept in both Nuclear Physics and Quantum Mechanics. Parity helps us explain the type of stationary wave function (either symmetric or asymmetric) that subatomic particles, like neutrons, electrons, or protons have.

In simple words, parity is the reflection of coordinates about the origin. For instance, the wave functions of x, y, and z are ψx, y, z.

 

Here, the wave function, ψ explains the stationary state of any particle, and x, y, z are the functions of the position.

Further, the parity is the transpose of  x, y, z as;

x  →  – x…..(1)

y  →  – y ….(2)

z  →   – z….(3)

To understand parity in particle Physics in detail, view this page till the end.

Conservation of Parity in Particle Physics

Now, let’s understand the parity conservation in particle Physics from the above three equations:

Assume that there is a three-axis coordinate system with x, y, and as coordinates. 

A point P lying on the coordinate plane has a position of P (x, y, z). Suppose that we shift the position of P to another point that is at its mirror image.    

Now, the coordinates of this point become P (- x, –  y, – z), i.e., the transpose of the original coordinates. We call this practice the transformation or reflection about the origin.

(Images will be Uploaded soon)

So, the changes we have made above are called Parity.

Certainly, we can state the definition of Parity into words:

Parity Definition

Above all, Parity is the reflection of the coordinates in a plane around the origin. Furthermore, parity helps us define the stationary state of the wave function.  

Further, parity can be explained in simple terms as;

Parity Particle in Physics

Now, let’s say, a parity operator “UP,” where “U” is the operator and “P” is parity.

Further, this  parity operator must follow the below property:

                        UP2  ….(a)

Similarly, the unity operator property is:

                  UP*  UPt =1……(b)

Indeed, the above equation (b) says that the product of the operator and the transpose of an operator is always unity.

Now, comparing equations (1) and (2), we get:

As a matter of fact, the transpose of an operator becomes equal to the operator itself, we call this property the Hermitian Property or Hermitian Operator.

Points to Note:

  • The value of parity operator UP must be one.

  • Also, the parity operator must be a unitary operator.

So, when the above two conditions are equal, we get what we call the “Hermitian Operator.” Besides, the condition of the Hermitian operator says that all its eigenvalues are real. Now, let’s understand the Parity of Elementary Particle:

Parity of Elementary Particle

Let’s say, a wave function  ψx, y, z  =  ψ(R), where the function “R = x, y, z.” 

Furthermore, when the wave function  is operated in the following manner, we get an eigenvalue “P;” 

                    UPψ(R)  = P  ψ(R)……(c)

Additionally, operating the function, we may or may not get the same function.  However, in the above case, the function is the same, i.e., ψ(R).           

Now, again operating the above equation (c) with a parity operator as;

                UP(UPψ(R)) =  UP(P ψ(R)) …..(d)

We know that the eigenvalue is always real and constant, so taking “P” out from equation (d), we have:          

               UP(UP< span>ψ(R)) =   P  . UP(R))

As we know from equation (c), UPψ(R)  = P  ψ(R), putting the same in equation (e), we get:

                  UP(UPψ(R)) =   P . P  ψ(R)

So, 

                  UP2 ψ(R) =  P2 ψ(R)

Since P is an eigenvalue and P2 = 1,therefore,

P    = ±1±1 ……(f)

The above equation (f) has two meanings, let’s understand these:

P = + 1

P =  – 1

What is the Significance of a Parity Operator?

Now, let’s see what even and odd parity is.

Considering a function, ψx, y, z on transposing, forms ψ– x, – y, – z.

On doing the transpose of ψ– x, – y, – z, we get “ψx, y, z“ again, which means, it is an even function.

However, if we get (- ψx, y, z ) in place of (ψx, y, z), it is an odd function.

When the sign of function remains the same, it is an even parity, i.e., (+ ψx, y, z).

Furthermore, when the sign of function remains the same, it is an odd parity, 

i.e., (- ψx, y, z ).

Parity Signs Explained

Let’s suppose that we change the coordinates of the stationary state of the particle.

However, on changing if we get the same function, it is an even parity, such as (ψ– x, – y, – z) remains (+ ψx, y, z) after a change. We call this function the symmetric function.

Moreover, if we get a different function, i.e., from (ψ– x, – y, – z) to ((+ ψx, y, z) after a change. We call this function an asymmetric function.

[Physics Class Notes] on Phase Mechanics Pdf for Exam

Phase, in mechanics of vibrations, is the fraction of a period (i.e., the time required to finish a full cycle) that to some extent completes after last passing through the reference or zero position. For example, the reference position for the hands of a clock is at the numeral 12, and therefore the big hand features a period of 1 hour. At [frac{1}{4}] past the hour, the big hand features a phase of one-quarter period, having skilled a phase of 900 or [frac{pi}{2}] radians. In this example, the motion of the big hand may be a uniform circular motion, but the concept of phase also applies to simple periodic motion like that experienced by waves and vibrating bodies.

Phase Mechanics

If the position yof an object, point or particle changes with respect to a simple harmonic motion, then the value of the position will change with respect to time t,according to the product of the amplitude, or maximum displacement, r, of the particle and a sine or cosine function composed of its angular velocity, denoted by the Greek letter omega (), the time t, and what is called the angle, symbolized by the Greek letter phi (Φ) : y = r sin (ωt +  Φ). The angle is known as the phase angle at any given time t, and the phase angle is equal towhen time is considered to be zero. 

According to phase mechanics, the phase itself is found to be a fractional value, i.e., the ratio of used time t to the total time period T, i.e., [frac{t}{T}], this ratio is equal to the ratio of the phase angle to the angle of the one complete cyclei.e., 3600 or 2 Radians. Thus, from phase mechanics, it is understood that the phase for uniform circular (or harmonic motion) has the value [frac{(ωt+Φ)}{2pi}]. Using these expressions to the illustrations of the moving minute hand quoted above, Φ is zero (which says that zero phase angle at zero time), and corresponding angular velocity is 2π radians per hour, and time t is [frac{1}{4}] hour, giving a phase of [frac{1}{4}].

While relating or comparing the phases of multiple periodic motions, such as waves, these motions are said to be in phase when corresponding points reach maximum or minimum displacements together or simultaneously. If the crests of two waves executing periodic motion cross the same point or the line simultaneously or in other words at the same time, then they are in phase for the given position. At the same time, if the crest of one and the trough of the other cross simultaneously, then the phase angles differ by 180°, or π radians, and the waves are said to be out of phase1800.

The determination of phase difference is of fundamental importance in bringing the change in current technology. In the diagram added below, we see that two curves represent the voltage or the potential difference (V) and the electric current (I) in an alternating current (AC) electric circuit with pure inductance (consisting of the only inductor). The difference in phase angle between the voltage and the current is found to be 900 i.e., the current and voltage curves are perpendicular to each other. From the analysis of the graph, the current is said to lag one-quarter cycle i.e., [frac{1}{4}] in phase. This lag in current can be observed in the diagram. In alternating current power transmission, the terms multi-phase and polyphase are employed to currents that are out of phase with one another. For example, in a two-phase system, we know that two currents are flowing with a phase-angle difference of 90°,similarly, in a three-phase system which is most commonly used in home appliance, the currents differ in phase angle by1200.

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Phase Mechanics Equation

The phase shift or the phase difference of a Sinusoidal Waveform is denoted by the angle Φ (Greek letter Phi), and the phase shift or the phase difference is measured in terms of degrees or radians that the waveform has changed from a particular reference point along the horizontal zero axes. In other words, the phase difference is the lateral (parallel) difference between two or more waveforms along a common axis. One of the interesting facts is the sinusoidal waveforms of the identical frequency sometimes will have a phase difference.

The phase shift of an alternating waveform usually range from between 0 to its maximum time period T(say) of the waveform during one complete cycle and this can be anywhere along the horizontal axis between, Φ = 0 to 2π (radians) or Φ  = 0 to 3600depending upon the angular units utilised.

The phase shift will also be represented as a time shift of in seconds describing a fraction of the time period, T for example, +30 mS or – 40 s but commonly it is more popular to express phase shift as an angular measurement.

Then the phase mechanics equation for the instantaneous value of a sinusoidal voltage or current waveform will be modified to take into consideration the phase angle of the waveform and this new general expression will represent the phase mechanics equation.

A = Amax sin (ωt [pmΦ])

Where,

A –The amplitude of the given sinusoidal wave

AmaxThe maximum amplitude of the given sinusoidal wave

ω –The angular frequency

Φ –The phase angle measured in either degrees or radians explains whether the given sinusoidal waveform has shifted to the left or right from the reference point.

Now, from the above expression, we notice that, if the positive slope of the sinusoidal waveform crosses the horizontal axis prior to time t = 0, then the waveform is said to be shifted to the left so Φ >0, and the phase angle will be positive in nature i.e., giving a leading phase angle. In other words, it develops earlier in time than00producing an anticlockwise rotation of the sinusoidal wave vector.

Similarly, if the positive slope of the sinusoidal waveform crosses through the horizontal x-axis after some time (i.e., after t=0) then the waveform is said to be shifted to the right so Φ <0, and the phase angle will be noted as negative in nature (-Φ) producing a lag in the phase angle as it appears following in time than 00producing a clockwise rotation of the sinusoidal wave vector. Both are the special cases elaborating lag and lead phenomenon and both special cases are presented below.< /span>

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Now, if we compare the phases of multiple sinusoidal waves, the periodic motions of the sinusoidal waves are said to be in phase when corresponding points reach maximum or minimum displacements together or simultaneously. If the crests of the sinusoidal waves executing periodic motion pass through the same point or the line simultaneously or in other words at the same time, then they are in phase for the given position. At the same time, if the crest of one and the trough of the other cross simultaneously, then the phase angles differ by 180° or π radians, and the waves are said to be out of phase 1800

To determine the phase difference, we require the frequency and period of the waves considered. For example, an electronic oscillator is producing sine waves of a frequency 200 Hz. Dividing the frequency by 1 gives the period, or the time taken to complete each cycle, so [frac{1}{200}]gives a period of 0.02 seconds

The Phase Difference Expression is Generally Given By:

PS = [frac{300ast Delta t}{T}]

Did You Know?

  • Estimating the phase difference between any two waves involves the comparison of two waves, and part of that comparison will be choosing which wave is considered as the first wave and which one is the second. 

  • In electronics, generally, the second wave is ideally the output of an amplifier or other device, and the first wave will be the input signal. 

  • In math, the calculation of the phase difference will be different than in the phase mechanics. In mathematics, the first wave may be an original function and the second a consequent or secondary function. For example, the first function may be y = cos x, and the second function may be y = sin xor vice versa. The order of the consideration of the waves will not affect the absolute value of the phase difference, but it will determine the polarity of the shift i.e, whether it is a positive phase shift or negative phase shift.

[Physics Class Notes] on Planck’s Constant Pdf for Exam

The energy was initially considered to be continuous. However, after a long research Max Planck came to the conclusion that the energy is not continuous in nature it is instead discrete and in small packets which are indicated by the small invisible particles called photons. These particles are the ones that carry the energy and this energy that has been carried is determined by Planck’s Constant. To know more about Planck’s Constant – value, Formula, Symbol, Applications, and Examples students can now check out more about the same via .

The energy that is released in the form of packets or chunks in a discontinuous manner is known as Photons where the energy of each photon is directly proportional to the frequency i.e. E and depends upon f.

                     E  ∝  f,   E = k x  h x u….(1)   (k is no of photons, and is an integer)

Here, ‘h’  is called the Planck’s constant.

On this page, we shall learn about the following:

  • Planck’s constant

  • Value of Planck’s constant

  • Deriving Planck’s constant formula in both MKS and CGS unit

  • Planck’s constant units and dimensional formula

  • Planck’s constant symbol

  • Applications of Planck’s constant with examples

  • Illustrative examples to understand the basics of this topic. 

What is Planck’s Quantum Theory all about?

A German theoretical physicist, Dr. Max Planck had put forth a theory known as Planck’s quantum theory. This theory states: Energy radiated or enwrapped is not perpetual, but in the form of packets called quanta. This energy is known as the “Quantum of energy.” For a single packet, we call it quanta, where quanta is an integer value, unlike continuous energy supply which has varying values: 1 or 1.1 or 1.2…

Packets are units of energy and they are called Quanta in general terms whereas Photons is a term used for packets in terms of visible light.

Consider this equation:

 E = h x c/λ….(2)

 h = 6.626 x 10⁻³⁴

 c = 3 x 10⁸ m/s

Put this value in the above equation(2)

(6.626 x 10⁻³⁴) * (3 x 10⁸)/λ

(19.878 x 10⁻²⁶)/λ  ∽   (2 x 10²⁵)/λ

We get,

M = (2 x 10²⁵)/λ

This is the value for energy of a single photon, and for ‘k’ no of photons, it would be:

The value of E is calculated only when wavelength, λ is given in meters. If λ is given in any other unit let’s say in Angstrom, simply, we can convert 1 Angstrom to meters (1 Angstrom = 10⁻¹⁰m) where h is the Planck’s constant, and h = Energy of a quantum of electromagnetic radiation divided by its frequency.

Planck’s constant ‘h’  is measured in Joule-seconds in the SI system.

       h  = 6.626 x 10⁻³⁴

and Electronvolt or (eV) in the M.K.S system.

1 eV  =  1.6 x 10⁻¹⁹ Joule 

E = (12400/λ) eV for λ in  Å. 

E = (1240/λ) eV for λ in nm.

 

Value for λ when E = 4.13 V 

E = 12400/λ

4.13 = 12400/λ

λ  = 12400/4.13 = 3000 Å

Experiments Used to determine Planck’s Constant:

There were two experiments that were used in order to determine the Planck constant and can be provided as follows:

1.Kibble Balance

2.X-ray crystal density method

  1. Kibble Balance:

It is the accurate weighing machine that was named after its inventor Bryan Kibble in 1975. It is designed to equalize one of the forces that arise with another. In this case, the weight of a test mass is exactly balanced out by a force that is induced when an electrical current is run through a coil of wire that has been immersed in a surrounding magnetic field.

  1. X-ray Crystal Density Method:

This method is a primary method that is used in the determination of Planck’s constant. Here crystals of silicon which are available in high quality and purity by the semiconductor industry are used.

What’s so Special about Planck’s Constant?

A blackbody is an idealized physical body, which assimilates all the electromagnetic radiation. Upon heating, it reflects the light falling on it, but that too of varying amounts of wavelengths.

(Image wil lbe Uploaded Soon)

(Image wil lbe Uploaded Soon)

Here in this graph, we can observe that less is the wavelength, lesser is the emission of waves, then a time comes when we get the maximum wavelength, Vmax, which means maximum emission.

The Vmax is the position shown as a peak in the graph is the visible light.

What happens here is when we go further, the wavelength keeps on increasing, but the emission of waves keeps on decreasing and continues further, we see that the emission of waves is negligible, but not zero. (All the wavelengths of whatever amount and irrespective of frequencies are radiated).

But from theoretical derivation, you must have observed in the curve that from the starting till the point when the wavelength is maximum, the graph shows symmetry, but what happens thereafter? The emission of waves is maximum even when the wavelength is less.

There’s a lot of difference when the wavelength is less. The modification in the above concept was brought up by a great German theoretical physicist, named Dr. Max Planck.

Where he considered light as a form of ‘k’ no of chunks or packets called photons by the relation.

E = k x h x f, k being the no of photons.

After his experimentation, the experimental and theoretical curves which were not symmetrical to each other, got into symmetry infers that the theory given by Dr. Planck was correct.

Summary

  • When an iron rod is heated, lights of all wavelengths are emitted, but a human eye can perceive only that light which is of maximum wavelength Vmax. 

  • We estimate the temperature of stars by observing the Vmax of the light emitted.