Category: Physics Notes PPT

Ohm is the unit of electrical resistance in the SI system. It was named in the honor of the famous German physicist Georg Simon Ohm. It is mathematically equal to the resistance of a circuit in which a potential difference of one volt can produce a current of one ampere or, the resistance in which one watt of power is dissipated when one ampere of current starts flowing through it. 

Ohm’s law provides a direct relationship between electric current and potential difference. The current which is flowing through any conductors is directly proportional to the voltage applied to it. In this topic we have discussed what is Ohm, let’s understand Ohm definition and laws and some numerical examples.

Ohm Definition

Ohm’s law states that the voltage across any conductor is directly proportional to the current flowing through it. Assuming all the physical conditions and temperature remain constant.

Ohm’s law is valid only if the temperature provided and other physical factors remain constant. Ohm’s SI unit is rho (Ω), In certain components, the current raises the temperature. Eg: The filament of a light bulb where the temperature rises as the currents are increased. In this case, Ohm’s law will fail. The lightbulb filament is violating Ohm’s Law.

Calculating Electrical Power Using Ohm’s Law

The rate at which one form of energy is converted from the electrical energy of the moving charges to some other form of energy Eg: mechanical energy, heat, magnetic fields, or energy which is stored in electric fields, is known as electric power. The electrical power can be calculated by using Ohm’s law and by substituting the values of voltage, current, and resistance.

When the values of current and voltage are given, the formula for finding power will be: P = V I

When the values of power and voltage are given, the formula for finding current will be: I = P / V

When the values of power and current are given, the formula for finding voltage will be: V = P / I

Experimental Verification of Ohm’s Law

Aim: To verify the Ohm’s law.

Apparatus Required: 

• Resistor

• Ammeter

• Voltmeter

• Battery

• Plug Key

• Rheostat

Theory: Ohm’s law states that the voltage across any conductor is directly proportional to the current flowing through it, Assuming all the physical conditions and temperature remain constant.

Procedure:

1. The key K is closed in the first step and the rheostat Rh is adjusted to get the minimum reading in the ammeter A and the voltmeter V.

2. The sliding terminal of the rheostat is then moved slowly to increase the current gradually and each time the value of current I flowing in the circuit and the value of potential difference V across the resistance wire is recorded. So, different sets of values of V and I are recorded.

Then for each set of values of Voltage and Current, the ratio V / I is calculated.

The ratio of V / I gives a constant value called R which is called the resistance of the conductor.

Plot a graph between current and the potential difference, it will be a straight line. This brings us to the conclusion that the current is proportional to the potential difference.

The Main Applications of Ohm’s Law are:

The main applications of Ohm’s law are:

• It is used to determine the voltage, resistance, and current of an electric circuit.

• Ohm’s law is majorly used in order to maintain the desired voltage drop across any electronic components.

• Ohm’s law is to find its application in dc ammeter and other dc shunts to divert the current.

Following are the Limitations of Ohm’s Law:

Ohms law has a certain limitation:

• Ohm’s law is not applicable for some electrical elements like diodes and transistors as they allow the current to flow through them in a single direction only.

• For those electrical elements which don’t follow linear relation with parameters eg: capacitance, resistance, etc the voltage and current won’t be constant with respect to time making it difficult to use Ohm’s law.

Solved Example

Example 1: If the resistance of an electric iron is 60 Ω and a current of 3.2 A flows through the resistance. Find the voltage between two points.

Answer: It is asked to calculate the value of voltage provided current and resistance have given to us: T, we use the following formula to calculate the value of V:

V = I × R

Substituting the values in the equation, we get

V = 3.2 A × 60 ÷ = 192 V

V= 192 V

Example 2: Calculate the resistance of an electrical circuit having a voltage supply of 100 Volts and a current of 10 mA.

Answer: V = 100 V, I = 10 mA = 0.010 A

R = V / I

= 100 V / 0.010 A

= 10000 Ω = 10 kΩ

There are many ways in which photons can interact with atoms, electrons and matter. Pair production is one among those, through which a photon can interact with the atoms and electrons. In pair production, a photon creates an electron and a positron in such a way that during this process the photon involved in the interaction will disappear. 

Basically, during the process of pair production, we are creating an elementary particle and its antiparticle with the help of a photon (or sometimes another neutral boson). Pair production is actually an exact opposite process of annihilation and it is useful in demonstrating the conservation of charges. Pair production is a chief method through which energy from gamma-ray is observed in a given condensed matter. Let us understand pair production, what is pair production along illustrations.

What is Pair Production?

Now, let us understand what is pair production. Before we start with pair production, let us have a look at the what is annihilation process. Both annihilation and the pair production process explain the interaction of photons with matter.

Annihilation

Electron-positron annihilation occurs when an electron and a positron (the antiparticle of the electron) collide. The result of the collision is the conversion of the electron and positron and the creation of gamma-ray photons or, less often, other particles. The process must satisfy a number of conservation laws, including:

• Conservation of charge. The net charge before and after is zero

• Conservation of linear momentum and total energy This forbids the creation of a single gamma-ray.

• Conservation of angular momentum.

So, now we will focus on what is pair production with the help of the annihilation process. When a gamma-ray photon interacts with any nucleus and it will lose its energy. Technically, pair production is a mode of interaction of gamma rays with the matter and during this process, they will result in loss of energy. During pair production, the energy of the incident photon will get converted into matter. The pair production can take place if and only if the energy of the photon is more than or equal to 102 MeV. 

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As positron is a highly unstable particle and has a very short lifespan, it will recombine with an available electron in the surrounding. The combination of a positron (the antiparticle of the electron) and an electron will lead to the formation of -rays which are at an angle of 180° to each other. The overall energy of initial -rays would be distributed equally i.e. for example if the original energy were 1.02 MeV then the two -rays (formed after the combination of the Positron and Electron) which are at an angle of 180° to each other would have 0.51 MeV of energy each. Any additional energy available will be conserved as kinetic energy in the produced particles.

Therefore, the pair production reaction is given by:

⇒Y ⟶ e^– + e⁺ ≃1.02 MeV

After understanding what is pair production we can note certain important facts about the pair production process as following:

• The pair production interactions are ruled by three major types of the law of conservation, i.e., conservation of total energy, conservation of momentum, and finally the conservation of electric charge. Soon after the collision, a pair of electrons and a positron will be created.

• In this collision, the antiparticle of an electron i.e., the positron (e+)as a particle, has the same physical properties which electron has, except its charge parity, these two particles, electron and positron have the opposite charge, and thus their magnetic momentum will also be of the opposite parity. Having an opposite charge parity means that the total sum of the net charge of pairs is zero, which is actually equal to the photon before the interaction. Therefore, the conservation of electric charge will be conserved and is evident.

• The momentum in the pair production can be ignored because the atomic nucleus is thousands of times more massive than just a pair of electrons and positrons, and thus, the photon momentum can be absorbed. Thus, it is possible to predict that absorbing momentum occurs without absorbing much energy. So, it is can be represented by an equation that shows the conservation of total energy and is given by:

⇒hv = E₊ + E_– = (Total energy of positron) + (Total energy of electron)

⇒hv = (m₀c² + K_–) + (m₀c² + K₊) 

⇒ hv = 2m₀c² + K_– + K₊………(2)

Where,

K₊ –The kinetic energy of Positron

K_– –The kinetic energy of the electron

Did You Know?

Do you know that the pair production can not take place in space!!!

Reason: The pair production can not take place in a vacuum or space. The pair production can happen only in the presence of an external object like an atomic nucleus which can experience some recoil during the collision process to conserve the energy and the momentum at the same time. Thus, the pair production can not take place in space or a vacuum, as the energy and the momentum can not be conserved at the same time.

In electromagnetic theory, there are two concepts known as permittivity and permeability. The concept related to the formation of an electric field is known as permittivity, and the one related to the magnetic field is known as permeability.

Definition of Permittivity

Permittivity can be explained as the ratio of electric displacement to the electric field intensity. It is the property of a material to measure the opposition generated by the material during the electric current development.

The permittivity of a material is represented by the symbol ε. The SI unit of permittivity is Farad per metre. The approximate value for permittivity is 8.85 X 10-12 Faraday/metre, which is found in a vacuum medium. The permittivity measures the number of charges needed for generating a unit of electric flux in a specific channel.

Permittivity is expressed in relative terms in engineering applications instead of absolute terms. The permittivity of free space (that is, 8.85 x 10-12 F/m) is represented by eo and the permittivity of substance in question (also represented in farads per metre) is represented by e. Here, the relative permittivity dielectric constant er, is given by:

[e_r  = frac{e}{e_o} ]

= e (1.13  x  1011)

Definition of Permeability

The property of the material which supports the formation of magnetic flux when passed through a magnetic field is known as permeability. It is affected by the field frequency, temperature, field strength, and humidity. It is represented by μ.

The permeability of the material is defined as the ratio of flux density to the field strength of a material. It is also directly proportional to the conduction of magnetic lines of force. The permeability of free space is also known as the permeability constant and is represented by μ0, which is approximately equal to 4Π X 10-7Henry/metre.

The symbol for permeability is μ. It is also defined as the ratio of the intensity of magnetic field (simple magnetic field) to the magnetic field (i.e., the limit to which the magnetic field can magnetize a material).

[mu = frac{text{Intensity of Magnetic Field (B)}}{text{Intensity of Magnetizing Field (H)}}]

or, [mu = frac{B}{H}]

Unit of Permeability

The unit of measurement for the intensity of the magnetic field is Tesla (T) or Newton per Ampere metre (N/Am).

Ampere per metre (A/m) is the unit of a magnetizing field.

Magnetic reluctivity is the reciprocal of magnetic permeability. The SI unit of permeability is given as Henries-per-metre (H/m). It is measured in Newtons-per Ampere squared (N/A2)

So as per the above permeability formula, it becomes unit Newton per Ampere square.

[mu = frac{Newton}{text{ Ampere Square}}]

Or [mu  = frac{N}{A^2} ]

By calculating their equations and units, we will find the dimension of permeability to be

[M¹L¹T^-2I^-2].

Difference Between Permittivity and Permeability

The main differences between permittivity and permeability are explained below.

From the above text, we understand that during the formation of electric fields, the obstruction produced by the material is measured by the permittivity. In contrast, the ability of the material to allow magnetic lines to conduct through it is known as permeability.

Development in technology has been quite synonymous with advances in physics, and this has, over the years, influenced society beyond our wildest imagination. The indelible role of physics in society is thus wholly undeniable. Such influences and subsequent advancements could broadly be categorized as falling under two major categories – Macroscopic and Microscopic. The microscopic influence includes all phenomena related to atomic, molecular, and nuclear advancements. The macroscopic consists of everything within the ambit of laboratory testing, practical effects and advancements, and astronomical associations. 

As evident, these two categories are overlapping at times, and it is only through a close association between these two areas that the age of technology, as we know it today, has come to be. 

How is Physics Related to Society and Technology?

The first significant influence that physics exerted in terms of technological development led to the introduction of the steam engine, which subsequently ushered the age of industrialization. The steam engine worked on the laws of thermodynamics and greatly improved the efficiency of engines for starters. The applications of thermodynamics have subsequently also been used in later inventions like refrigerators, blowers, vehicles, etc. Here are some of the ways physics has left its impression on society through technological advancements.

1. Energy Industry 

The contributions that physicists like Faraday, Tesla, and Edison had on the commercialization of electricity is undoubtedly exceptional. They kick-started what is today called the age of globalization. The use of fossil fuels like petrol, diesel, coal changed everything from how the food was produced to how people travelled from one place to another. The influence was so prolific that it is difficult today to name an industry that wasn’t influenced for the better, through these developments. 

With increasing awareness about the growing levels of pollution today, the world has shifted to alternative and renewable sources of energy. Even this gradual shift is being overwhelmingly influenced by physics. Dams, solar panels, wind farms, nuclear reactors – the energy of the future is overwhelmingly dominated and influenced by the physics of today. 

2. IT Industry 

The IT industry has been spearheaded by the extensive proliferation of computers in our daily lives, thus giving rise to the modern MNCs as we know them today. While the computer may not have been developed exclusively on the foundation of physics, the subsequent infrastructure, including the once ancillary but now vital data processing and network speeds, have been largely contributions of physics. 

For starters, John Bardeen was instrumental in the development of transistors and the theory of superconductivity, factors that led to the development of the early computer. The use of lasers was pioneered by C.H. Townes, which is now used from microsurgery to the most commonly used computer mouse. Even the use of optical fibres is based on the principle of total internal reflection of light. Optical fibres ensure better connectivity speeds and minimal data loss, thereby ensuring faster processing speeds and better reception of signals.

3. Medical Industry

In the medical industry, physics has been especially essential in radiology. W.K. Roentgen discovered X-rays, which is today the most popular, conclusive, and inexpensive method of determining fractures in the body. Ultrasonography works on the principle of reflection of ultrasonic waves and forms an essential part of both the medical as well as the defence industry. 

Another singular influence has been the use of nuclear medicine to cure diseases. Nuclear medicine today includes therapies that use radioactive elements to treat conditions like hyperthyroidism and certain types of lymphoma. 

4. Communications Industry 

In this case, by the communications industry, we refer both to the telecom and television industry, which has connected the world digitally, as well as the commercial vehicular industry like airlines which has made physical travel between places extremely easy. Telephones and televisions operate on the principle of electromagnetic waves. The generation of electromagnetic waves was first shown by the German physicist Heinrich Rudolf Hertz. Aeroplanes, on the other hand, at the fundamental level, operate on Bernoulli’s principle. 

5. Contributions that Went Beyond a Single Industry

There are various other discoveries that physics propagated that went on to change society in more ways than one. These include:

• Principle of levers and carriers – Archimedes

• Galilean Telescope, Gaseous Thermometer – Galileo Galilei

• Geometric Optics – Johannes Kepler

• Law of Elasticity – Robert Hooke

• Expanding nature of the universe – Edwin Hubble

Physics also helps us understand other disciplines like geology, agriculture, chemistry, biology, and environmental science. Astrophysics and cosmology, the two branches of physics help in expanding our vision into the universe.

Conclusion

Thus, physics helps improve the quality of our life. Physics is necessary for the development of new gadgets. Most of the modern gadgets used in our homes make use of Physics to form and function. Understanding Physics makes us understand the world surrounding us. It also helps in the development of new techniques for medical applications, such as computer tomography, magnetic resonance imaging, positron emission tomography, ultrasonic imaging, and laser surgery.

This makes Physics touch all areas of our lives and illuminate them all. This brings to light the value of Physics in our life. Therefore, all educational institutes should and do promote the study of Physics and provide the necessary infrastructure for study and research in this field.

The length of the path travelled by a car moving from one point to another point is called distance and the distance travelled is also known as the path length. However, if it takes the shortest path, it becomes the  displacement. We can also say that the difference between the initial and final position of a car is its displacement. 

But before we move forward let us know what motion is. If we look around, everywhere we can see objects moving. Kids play, birds fly, animals move in search of food, people walk or run, vehicles run on the road, river flow, etc. So basically, we can find motion everywhere in the universe. But what is meant by motion?

If you notice the above-mentioned instances they all move from one place to another and change their place. Therefore, motion is nothing but change in the position of a body with respect to time. If a body is at rest, it means that the body is not in motion, merely means that it is being described concerning a frame of reference. 

Position – Understanding with an Example

To describe the motion of an object, you must know and be able to describe its position.

Let us understand this with an example, let us say Ram moved from point R to S. This means Ram’s initial/previous position was R from where he shifted to S after sometime. Now the question is how can we represent Ram’s initial position? 

In physics, we specify a position with the help of a reference point and a set of three mutually perpendicular axes or  rectangular coordinate systems. They are the X, Y, and Z-axis. The reference point is known as origin; it is the intersection of the above three-axis (X, Y, and Z). So we take point R as the reference point or origin with coordinates (0, 0, 0) and S is represented by a set of coordinates on the three-axis (X, Y, Z).

Since we know that motion is the change in position with time, we install a clock in this system. The coordinate system along with the clock is the frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of the object are described. Thus, if one or more coordinates of a body change with time, the body is said to be in motion.

Path Length

The path length is the actual length of the path traversed by the body between the Initial and Final positions.

Displacement – Understanding with an Example

It is the shortest length i.e. Straight line distance between Initial and Final positions. Displacement is a vector quantity.

Displacement formula:

If s_i is the initial position of an object and s_f is the final position, then the displacement of this object is:

s  = s_i – s_f

Here, s is a variable referred to as displacement.

Since displacement has magnitude and direction, it is a vector quantity and the path is a scalar because it has only and no direction.

Explanation with Examples

To have a proper understanding of the position, path length, and displacement and the difference between them. Follow are some examples given with explanation:

Let us take three examples here. In the first one, Ram starts travelling from point R of the square path RSTU with RS = 1 km. He travels through S, T, U, and comes back to R in 20 minutes. The distance travelled by him is 4 x 1 km = 4 km. But if you see the change in his position from the start to the end of the journey, it is nil (It has no change). Ram started at point R and came back at R.

In the second example, 

Ram travels from Point R to S along the straight line in 60 minutes. The distance travelled by him is 5 km. And the total distance from the start to the endpoint travelled by Ram is also 5 km.

Now in the third example, Ram travels through the triangular path. He starts from point R and reaches T through point S in 120 minutes. The distance that has been travelled by him is 3 km + 4 km = 7 km. But if we see how far he is from the point where he started his journey, it is 5 km.

If you notice the above examples, the distance travelled and the change in position may or may not be the same.

The distance travelled by the body is known as the path length. Whereas the change in position, that is the difference between the initial and final positions of the body is called its displacement.

Hence, the path length is 4 km but the displacement is 0 in the first case.  The path length is the same as the displacement – 5 km in the second example and the third example, the path length is 7 km but the displacement is 5 km.

From the above text, we understand that the position of an object describes the point at which the object is standing at an instant. The change in position describes that an object is set into motion and this distance travelled is the path length. Also, if an object takes the shortest path, it is displacement.

Precession meaning in physics is the change in orientation of a rotating body with respect to its rotational axis. Precession in a sentence can be defined as the rotational movement in the rotational axis of a rotating object. The phenomena of precession are closely associated with the action of a gyroscope or a spinning top. It refers to the slow rotation of the axis of rotation of a rotating or spinning object about a line intersecting the spinning axis. The movement of astronomical objects on their orbits and the slow and circular movement of a spinning top can be referred to as precessional motion. 

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Types of Precessional Motion

In physics, precession movement is basically of two types: torque-free and torque induced. Let us study in detail both the precessional motions.

Torque free Precession: In precession, torque-free signifies that no external force or torque is applied on the rotating object. In this kind of precession movement, the angular momentum is constant, but the angular velocity changes with time. The change in the body’s angular velocity in torque-free precession is brought about by the moment of inertia. 

The following formula can calculate the torque-free precessional motion of an object spinning about an axis:

ωp = Isωs / Ip cos (α)

Where ωp denotes the precession rate, ωs denotes the spin rate about the axis of symmetry and Is denotes the moment of inertia along the axis. Here, α denotes the angle between the moment of inertia and axis symmetry.

Torque Induced or Gyroscopic Precession: In physics, gyroscopic precession definition is the phenomenon in which the axis of a gyroscope or any other spinning object describes a cone in space when an external force is applied on induced into the object. The phenomena of torque induced precession can be observed primarily on spinning toy tops and gyroscope, and this is why it is named gyroscopic precession.

The torque induced or gyroscopic precession can be explained by understanding the movement of a spinning top, which is discussed in detail below:

In a spinning top, the weight of the top acts downwards from its centre of mass when it is in a rotational motion. The normal force of the ground acting upon the top pushes it when it comes in contact. The weight and the force of the ground act on the spinning top to produce torque and bring about precession. 

Newtonian Precession 

According to classical Newtonian theory, precession can be defined as the change of angular velocity and angular momentum produced by torque. The equation which relates the torque to the change of angular momentum is as follows:

T = dL/dt

Here, L represents the angular momentum, and t represents the torque. 

Relativistic Theories

As a correction to the Newtonian precession theory of gyroscope, the theory of relativity gives three corrections, namely;

Let us discuss all three corrections.

Thomas Precession: The Thomas precession is given by Llewellyn Thomas for an object that is being accelerated along a curved path. The Thomas precession can be defined as a motion of the spin axis of an electron caused by the interaction between the electron and the electric field of the nucleus of an atom. 

De Sitter Precession: The De Sitter Precession is a general relativistic correction given for the classic Newtonian precession theory. This correction is given by William de Sitter and is known as the Geodetic effect or Geodetic precession. This theory represents the effect of the curvature of spacetime given by the general relativity theory. The theory explains the precession movement of a spinning body near a large non-rotating mass. 

Lense-Thirring Precession: It is also a general relativistic correction given to the Newtonian precession theory. The correction explains the movement of a spinning object on a curved path with a large rotating mass nearby. This theory is also called the gravitomagnetic frame-digging effect. 

Orbital Precession

In astronomy, precession has a different meaning. In astronomy, precession meaning can be defined as the slow changes that occur in heavenly bodies, and it is also called orbital precession. An example of precession in astronomy can be the steady change in the orientation of the earth’s axis of rotation, also known as the precession of equinoxes.

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