Category: Physics Notes PPT

Electronic devices function on a tank circuit to enable the sharing of information. Generally, an amplifier with a sinusoidal input attains an amplified output signal. In a feedback amplifier and transistor oscillator, the oscillator generates an amplified output signal without any intake of input signals. The working of an oscillator is a repetitive process with the amplified input and output resulting in feedback with persistent operations. This ensures the transmission of information signals back and forth in an electronic device without any interval.

This infers a single input lead with endless outputs based on the feedback and frequency regulated, the external signal delivers an alternating current which is self-sustainable.

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Types of Feedback Amplifiers

In the working of an oscillator, feedback refers to the ability of the output signal to return to the input. There are 2 types of feedback amplifiers:

1. Positive Feedback Amplifier

As shown in the image, Vin is the input signal sourced through the transistor to Vout is the output, further, the succeeding network formed with the sourcing of Vout back to Vin is positive feedback indicated with Vf in the figure. These positive feedback amplifiers are utilized for oscillations. 

2. Negative Feedback Amplifier

On the contrary, a negative feedback amplifier indicates the incapacity of the (Vout) output signal to return to the (Vin) input signal.

Types of Transistor Oscillators and Functions

Let’s quickly take a look at some types of transistor oscillators and how they function.

1. Working of Colpitts oscillator

A variation of an oscillator tank circuit formed with 2 capacitors and 1 inductor. Its connectivity can be achieved in series allowing the inductor to be placed in a parallel position to the capacitors.

The working of the Colpitt oscillator was invented in 1918 and named after scientist Edwin Colpitts. As compared to the working principle of the Hartley oscillator, it stimulates preferable frequency stability.

2. Working Principle of Hartley Oscillator

Hartley Oscillator is a tank circuit composing 2 inductors and one capacitor. The inductors are linked in a combining series whereas the capacitor is positioned parallel to the series of inductors. It was invented in the year 1915 and named after an American scientist Ralph Hartley. It generally operates with frequencies ranging from 20 kHz to 20MHz.

3. Working of Wien Bridge Oscillator

A Wein bridge oscillator is a bridge circuit formed with 4 resistors and 2 capacitors. It produces sine waves with largely ranging frequencies. The working of the Wien bridge oscillator was formulated and named after Max Wein in the year 1891 for measuring impedances.

Now that we have analyzed and understood the functioning of feedback amplifier and transistor oscillator, we’ve comprehended the functioning of varied oscillations like the working of Colpitts oscillator, working principle of Hartley oscillator, and working of Wien bridge oscillator.

One of the factors that remain constant is the positive feedback gained to achieve repetitive and long-term processing of signals.

4. Clapps Oscillator.

The Clapps oscillator consists of three capacitors and an inductor that is already set to the oscillator frequency. The Clapps oscillator is also known as the Gouriet oscillator. This is named after its founder James Klinton Clapp. Although, it is said that these kinds of oscillators were built by several independent persons. One among them was Gouriet. The Clapps oscillator has excellent frequency stability.

5. Robinson Oscillator

The Robinson oscillator is a further development of the already existing marginal oscillator. It is therefore often referred to as marginal Robinson oscillator. A British physics scientist named Neville Robinson is behind the invention of this oscillator.

6. Dynatron Oscillator

The dynatron oscillator was invented by a scientist named Albert Hull in 1918.

Like the Clapps oscillator, the dynatron oscillator also has better frequency stability. The dynatron oscillator can oscillate between a huge range of frequencies and this can be counted as one of its many advantages.

7. Phase Shift Oscillator

A phase shift oscillator is a combination of inverting amplifiers, resistors and capacitors. These oscillators are also called auto oscillators as they are mainly used for audio frequencies.

8. Pierce Oscillator

The Pierce oscillator is derived from the existing Colpitts oscillator. The name of the oscillator is kept after its inventor George. W. Pierce.

The components of the pierce oscillator are one resistor, two capacitors, and a quartz crystal. All the digital clocks are run by a Pierce oscillator. It is a quartz oscillator.

9. Optoelectronic Oscillator

The optoelectronic oscillator is also known as OEO and is based on the concept of transforming light energy into microwave signals. The optoelectronic oscillator is known to have stability as well as a high-quality factor, among various other factors that aren’t generally found in basic electronic oscillators. This type of oscillator also has photonic components and is known to operate at high speed. It is an optoelectronic circuit known to modulate optical continuous wave signals.

10. Armstrong oscillator

The Armstrong oscillator was invented by a US engineer named Edwin Armstrong and other Australian engineers Alexander Meissner. However, both of them have invented it independently, so the oscillator is also named the Meissner oscillator. The feature that makes it unique is the tickle coil that is used, hence sometimes it’s also called a tickler oscillator. This electronic oscillator uses a combination of a capacitor and an inductor to produce oscillations.

Solved Example

Answer- Positive feedback adopted in the working of an oscillator stimulates an output frequency without the implementation of any input. Positive feedback boosts the output signal by charging a quicker and higher signal in the direction of the input. It functions in a loop permitting continuous and undamped oscillations. Following the principle ‘more produces mo
re’ it is utilized in procedures like fruit ripening and contractions in childbirth. Amplification in an oscillator only administers with positive feedback as it feeds the output signal back to the input to model it to be in phase, further the feedback and input enhance the amplifier.

Did You Know?

• A classic based on feedback control theories published in 1868 was the first-ever written theory relating to feedback by James Clerk Maxwell as a popular paper named ‘On governors’.

• The verbal application of the word ‘feedback’ was implemented in the US in the 1860s, however, the official usage of the word ‘feedback’ as a noun was witnessed in the year 1909 by Nobel laureate Karl Ferdinand Braun referring to bonding of the elements in an electronic circuit.

Fluid is defined as a substance with no fixed shape and yields easily to external pressure. But one of the major features of all fluid is its ability to flow. The fluid includes gas and liquid. This chapter talks about the mechanism behind fluid flow.

Fluid Mechanics

Fluid mechanics talk about the implementation of the fundamental laws of physics such as that of principles of mechanics and thermodynamics including conservation of mass, conservation of energy and Newton’s laws of motion on the behavioural pattern of fluids viz liquid and gas. Fluid mechanics is broadly classified into two categories:

a) Hydrostatics or fluid statics- revolves around the study of fluid at rest

b) Hydrodynamics of Fluid Dynamics – the study about the fluid in motion

This chapter focuses on the fluid dynamics part with special emphasis on fluid behavior under dynamic conditions.

Fluid Flow

Studying fluid motion is very complicated. But in order to understand the basics of fluid flow certain assumptions have been made about the fluid to simplify the situations. While studying fluid flow, we always consider the fluid to be an ideal one. The assumptions made for an ideal fluid include:

a) The fluid is incompressible and thus with a constant density

b) The motion is irrotational that is there is smooth flow(either laminar or streamline), devoid of any turbulence

c) The fluid is non-viscous without any internal friction

d) The flow is steady i.e the velocity at each point is constant in time

The flow of fluid can be broadly classified into two categories :

1. Laminar flow

2. Turbulent flow

In a laminar flow, all the particles of a fluid within a layer move at the same rate. On the other hand, the flow is considered turbulent if the critical speed of a fluid is obtained.

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Conceptually, fluid flow can be considered analogous to the transport process, in which the rate of transfer of matter or energy is dependent on physical factors like the physical properties of the material that has been used (body through which the fluid is moving) and the geometry of that system. Some of the fundamental principles of physics that are considered to study fluid flow are:

These three conservation laws will form the basis to develop our fundamental understanding of Fluid Flow. Gradually, we will apply these fundamental principles to derive the three major mathematical descriptions of Fluid Flow: the Continuity Equation, Bernoulli’s Equation, and the Momentum Equation. But we need to keep one thing in mind all the time that the fluid considered here is the ideal one. We will try to understand the mechanism of flow of fluids through vessels of various shapes and sizes.

1. Conservation of Mass/Continuity Equation

The basic principle of classical physics is mass is neither created nor destroyed. It is one of the fundamental laws governing fluid motion and it will pave the way for our understanding of fluid dynamics. The figure below shows an infinitesimally small stationary, rectangular control volume. Let’s assume a fluid is moving through this. This type of control volume which has its surface fixed in space is called a Eulerian control volume.

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The fluid velocity vector has componentsU(vector)=U, V, W in the directions x (vector)=x,y,z and lets the fluid density be ρ. In case of a general, unsteady, compressible flow, all four flow variables may vary depending on position and time. The law of conservation of mass over this control volume can be formulated as:

[[{text{Rate of mass accumulation inside the control volume}}] = [{text{Rate of mass flow into the control volume}}] – [{text{Rate of mass flow out of the control volume}}]]

2. Conservation of Energy

The concept of conservation of energy during the flow of a fluid can be explained by Bernoulli’s equation. We will find that for a fluid (e.g. air) flowing through a pipe with a constriction in it, the fluid pressure is least at the constriction. In terms of the equation of continuity, the fluid pressure falls with the increase in the speed of flow. The reason behind this is explained by the equation. The fluid has different speeds with different kinetic energies at different parts of the tube. The changes in energy are the outcome of work being done on the fluid and the only forces in the tube that work on the fluid are the driving forces related with changes in pressure from place to place.

This equation is concerned about three issues:

a) Conservation of energy during the flow

b) A pressurized fluid must contain energy by the virtue of which the work must be done to establish the pressure.

c) Energy change happens simultaneously with the pressure change in a moving fluid.

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Let m be the mass element that moves from (1) to (2)

m = ρ A₁ ∆x1 = ρ A₂ ∆x2 = ρ ∆V where ∆V = A₁ ∆x1 = A₂ ∆x2

As per the Equation of continuity, AV = constant 

 A₁ v₁ = A₂ v₂ A₁ > A₂ ⇒ v₁ < v₂

Since v1 < v2 the mass element has been accelerated by the net

force

 F₁ – F₂ = p₁ A₁ – p₂ A₂

Mass element faces an increase in KE

 ∆K = ½ m v₂² – ½ m v₁²

 = ½ ρ ∆V v₂² – ½ ρ ∆V v₁²

The mass element has an increase in GPE

 ∆U = mg y₂ – mg y₁ = ρ ∆V g y₂ = ρ ∆V g y₁

The increase in KE and GPE is generated from the network done on the mass element by the forces F₁ and F₂ (the sample of mass m, inmoving from a higher pressure region to a lower pressure zone, has some positive work done on it by the surrounding fluid)

[W_{net} = F_{1} Delta x_{1} – F_{2} Delta x_{2} = p_{1} A_{1} Delta x_{1} – p_{2} A_{2} Delta x_{2}]

[W_{net} = p_{1} Delta V – p_{2} Delta V = Delta K + Delta U]

[p_{1} Delta V – p_{2} Delta V = frac{1}{2} rho Delta V v_{2}^{2} – frac{1}{2} rho Delta V v_{1}^{2} + rho Delta V g y_{2} – rho Delta V g y_{1}]

Rearranging

[p_{1} + frac{1}{2} rho V_{1}^{2} + rho g y_{1} = p_{1} + frac{1}{2} rho V_{2}^{2} + rho g y_{2}]

We can also conclude that for any point along a flow tube or streamline

[p + frac{1}{2} rho V^{2} + rho g y = {text{constant}}]

This is what is called the Bernoulli’s theorem. 

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Bernoulli’s theorem is applicable only to an ideal fluid. Bernoulli’s Principle can’t be used when the viscosity is substantial for the fluid in motion. It can be applied to gases as well provided there are only small changes in pressure.

3. Conservation of Momentum/Momentum Equation

From Newton’s second law of motion, it has been found that if momentum is gradually decreasing with time, then d (mv) /dt is negative and the force responsible f
or the change is also negative. This is the force acting on the body resulting in changing momentum. Again, following Newton’s third law of motion, there is the equal and opposite force exerted by the body. But if we want to apply this principle of conservation of momentum to fluid flow, we will be struck by two difficulties, as compared to the application of conservation of mass and energy. Firstly, momentum as a conserved quantity is comparatively less familiar to us than mass or energy – we will have slightly more difficult to analyze what exactly is happening. Secondly, and most importantly, both mass and energy are scalar quantities that have magnitude only, unlike momentum which is a vector quantity with both magnitude and direction. Momentum needs to be conserved in a particular direction, so we must be well sensitive to the directions in which various forces are acting and also be careful about the direction of the components moving, and we must (to understand more advanced applications) be able to perform the calculations keeping in mind the several directions simultaneously. With the application of Newton’s Second Law, the product rule gives a form more appropriate for the analysis of fluid flow:

[F = frac{d(mv)}{dt} = m frac{dv}{dt} + v frac{dm}{dt} = ma + dot{m}v]

where [dot{m}] has been considered as the rate of change of mass (i.e. the rate at which mass comes in or leaves a control volume). Mostly we are focussing on the steady flow, that is it has zero acceleration, and thus we can say, F = ˙mv. As mentioned above, the momentum force exerted by the fluid, in turn, is of the same magnitude, but just in the opposite direction.

Fluid flows has a crucial role to play in a vast variety of phenomena be it natural or manmade systems. In a way or the other, the mechanics and thermodynamics of fluid flow have impacted energy generation, various atmospheric creations, 

manufacturing of various vehicles and flights and many more activities. This chapter has attempted to give an overview of fluid dynamics with a special focus on the fundamental principles of fluid mechanics. But one thing should be kept in mind that under a couple of circumstances we have considered a few facts but in the real implementation, there may arise a few issues as there is nothing called ideal fluid.

Force is the cause of change in the state of motion of a body or an object. It is a quantitative description of an interaction that causes a change in an object’s motion. Force can cause an object to move or accelerate, to slow down or decelerate, to stop, or to change its direction. The applied force can be a push, a pull, or dragging of an object.

Examples of Force in Everyday Life

1. Applying brakes to stop a vehicle

2. Lifting a load

3. Pushing and pulling a door 

4. Kneading and rolling the dough 

5. Kicking a football 

6. Stretching a spring or a rubber band 

7. Attracting paper bits with an electrostatically charged comb

8. Force exerted by our muscles while moving the limbs 

9. Throwing a stone in the air and it’s coming down.

10. A magnet attracting iron nails

The State of Motion and Causes of Change in Motion

Motion is the change in position of a body with respect to its surrounding environment, within a given interval of time. An object is said to be in motion if its position changes with time, with reference to a fixed frame.

A chair cannot move its own, what do you do to make a chair move?

We often say that a force has been applied to the chair when it is pushed.

The motion of an object is explained by its speed and direction of motion. If an object is at rest, the state is considered to be in the state of zero. By applying force, we can change the position of the object or can say that the object is in motion. 

While taking a penalty kick in football, before being hit, the ball was at rest. Then, its speed was zero. The player applied force on the ball. This applied force sets the ball in motion towards the goal.

Suppose, the ball hits the goal or the goalkeeper dives and saves the goal. In both conditions, the speed of the ball changes. Force can also cause an increase or decrease in motion if it is applied in the same direction or the opposite direction respectively.

Many times, an applied force may not result in any change in the state of motion.

What will happen when you push a wall with the maximum force that you can exert? 

No effect of force is observed.

How can Force Change the State of Motion?

1. The Applied Force can Cause Acceleration

The change in motion is equivalent to a change in velocity. A change in velocity applies that there will be an acceleration. The force causes a change in motion. So it produces acceleration too.

If an object is stationary in the beginning, it accelerates when it starts to move. Likewise, if an object is already moving and a force is applied in the same direction, the object will accelerate as long as the force is applied to the object. If the force is removed, the acceleration will also stop.

For example, James was walking towards the north at a speed of 10 metres per second. James speeds up and now begins running towards the west at 20 metres per second after 5 seconds. In this case, James has accelerated his velocity by 2 m/s² i.e his velocity has increased by 2m/s every second. 

Another example is of an apple falling down. It starts falling at zero metres per second. At the end of the first second, the apple is moving at 9.8 metres per second. The apple has accelerated. This acceleration here is caused by gravity.

2. The Applied Force can Cause Deceleration

If an object is moving and a force applied to it in the opposite direction of the motion, the object will decelerate or slow down.

Suppose, a cricketer hits the ball high up. It will slow down as it travels upwards due to the force of gravity. Likewise, a boat decelerates due to wind flowing opposite to the direction of motion of the boat.

Decelerating force can put a moving body to rest.

For example, when a car driver applies brakes, it begins to decelerate.

3. Force can Cause a Change in the Direction of Motion

A change in either the speed of a moving body or its direction or both are referred to as a change in its state of motion. Thus, the force can change the direction of motion.     

For example- In a cricket match, a bowler bowls the ball towards the batsman with some velocity(u). The batsman hits the ball and it travels in a different path with another velocity(v). This is because the batsman applies force on the ball and changes the direction of the ball.

Newton’s Laws of Motion

Newton the great physicist gave laws of motion that are useful in everyday lives. The three laws of motion are described below.

1. Law 1:- The first law of motion tells that an object will remain at the state of rest or continue to move at a certain speed unless an external force is applied on the object, which will violate the equilibrium of the system. The first law of motion by Newton is also called the “law of inertia” and it explains the concept of inertia, application of the force, and inertial frame of reference.

2. Law 2:- Newton’s second law is the quantitative description of the changes that force may induce in the object on which the force is applied.

This entails that when a force is applied on a given object of constant mass, the rate of change of the speed of the object will be directly proportional to the total force applied on the object. In simpler words, the acceleration produced in the object due to the application of the force will be directly proportional to the force applied.

i.e. Force applied ∝ acceleration produced

F ∝ a    F = Ka  and K here is the mass so 

F  = ma      or

Force applied = (mass of the object) (Acceleration produced in the object)

3. Law 3:- The third law of Newton states that for every action or force, there will be equal but opposite reactions or force. If you push the wall, the wall does not move as it exerts an equal and opposite reaction force. This law is commonly called the law of action and reaction in physics. 

Example:- If a book is lying on a table, which can be interpreted as the book is applying force equal to its weight on the table, according to this law, the table applies an equal and opposite force on the book which will counter the force of weight applied by the table.