Category: Physics Notes PPT

Wherever there is a flow of charged particles, we say that it is an electric current. The flow of electricity is always stable and constant. You will find that it flows from higher potential to lower potential in a circuit. A regular circuit contains conductors (usually copper wires), resistors, switch to turn on and off the circuit, and a power source. A resistor is an electrical component that provides resistance or limits the flow of current in the circuit. For example, we can consider a tube light used in our household as a resistor.

In general use, we have a combination of resistors used in all circuits. We can either have resistors in series or resistors in parallel. In some cases, we can have both series and parallel combinations of resistors in a single circuit.

The above figure shows a simple circuit consisting of a conductor, a resistor, and a battery.

Series Combination of Resistors

When we have resistors in series, the current flows through them one after the other. Each resistor will have the same current flowing through them. Across a series of resistors, there will always be a voltage drop.

To calculate the equivalent resistance, we need to derive the series resistance formula. To obtain the equation, we use Ohm’s law. According to the law, the potential drop ‘V’ is given as V=IR, where ‘I’ is the current, and ‘R’ is the resistance of the circuit. 

The image shows the circuit of resistors placed in series.

According to Kirchhoff’s loop law we have,

[sum_{i=1}^{N}]   [V_{i}] = 0

V − V1 − V2 − V3 = 0,

V = V1 + V2 + V3

V = IR1 + IR2 + IR3

I = VR1 + R2 + R3 = VRS

Therefore, we get the series resistance formula as,

RS = R1 + R2 + R3 + . . . + RN−1 + RN

[R_{s}] = [sum_{i=1}^{N}]  [R_{i}]

Parallel Combination of Resistors

When we have resistors in parallel, the electric current divides itself to travel through the different branches. The voltage drops across each resistor will be equal, unlike the resistors in series. Since there are a lot of resistors connected in parallel, we must find the total resistance. To do that we need to derive the resistors in the parallel formula. To acquire the equation, we use Ohm’s law. According to the law the equation for the electric current ‘I’ is given as I = V/R, where ‘V’ is the potential drop, and ‘R’ is the resistance of the circuit. 

The image shows the circuit of resistors placed in series.

According to Kirchhoff’s junction rule we have,

[sum] [I_{in}]  = [sum] [I_{out}]

I = I1 +I2

I =  [frac{V_{1}}{R_{1}}] +  [frac{V_{2}}{R_{2}}] = [frac{V}{R_{1}}]  +  [frac{V}{R_{2}}]

I = V  [left ( frac{1}{R_{1}} + frac{1}{R_{2}} right )]

[R_{p}] =  [left ( frac{1}{R_{1}} + frac{1}{R_{2}} right )^{-1}]

Therefore, we get the resistors in the parallel formula as,

[R_{p}] = [left ( frac{1}{R_{1}} + frac{1}{R_{2}} + frac{1}{R_{3}} +  cdots + frac{1}{R_{N-1} + frac{1}{R_{N}}} right )^{-1}]

 [R_{p}] = [left ( sum_{i=1}^{N} frac{1}{R_{i}} right )^{-1}]

Combination of Resistors In Series And Parallel

In practice, you will never find simple electrical circuits, where the resistors are only placed in series or parallel. Instead, you will find complex connections with multiple resistors connected in series and parallel at the same time. Now, just because the circuit looks complicated, it doesn’t mean that it is difficult to calculate the resistance of the circuit. All you need to do is break the connections into small parts so that you can calculate the equivalent resistance easily. Your main goal is to keep decreasing the number of resistors by using the formula of resistance in series and parallel. We will now try to solve some questions on resistors in series and parallel.

Solved Problems

Question 1) Consider a circuit with a voltage of 9V, and consisting of five resistors. Calculate the equivalent resistance, and the current ‘I’ through the resistors.

Answer 1) Looking at the figure, we can see that the resistors are in series. Therefore, we will use the series resistance formula to calculate the equivalent resistance.

Given: V = 9V

R1 = R2 = R3 = R4 = 20Ω

R5 = 10Ω

The equivalent resistance is given as,

RS = R1 + R2 + R3 + R4 + R5 = 20Ω + 20Ω + 20Ω + 20Ω + 10Ω = 90Ω

The total resistance with the correct number of significant digits is Req = 90Ω.

Using Ohm’s law, we can calculate the current in the circuit.

I = V/RS = 9V/90Ω = 0.1A

Question 2) Three resistors R1 = 1.00Ω, R2 = 2.00Ω, and R3 = 2.00Ω, are connected in parallel. The battery has a voltage of 3V. Calculate the equivalent resistance, and current ‘I’ through the circuit.

Answer 2) Since the resistors are connected in parallel, we will use the resistors in parallel formula to calculate the equivalent resistance.

Given: V = 3V

R1 = 1.00Ω

R2 = 2.00Ω

R3 = 2.00Ω

The equivalent resistance is given as,

 [R_{p}] =  [left ( frac{1}{R_{1}} + frac{1}{R_{2}} + frac{1}{R_{3}}  right )^{-1}] 

 [R_{p}] =  [left ( frac{1}{1} + frac{1}{2} + frac{1}{2}  right )^{-1}] 

[R_{p}]  =  0.50Ω

Therefore, we get the equivalent resistance as [R_{eq}] = 0.50Ω.

Using Ohm’s law, we can calculate the current in the circuit.

I = V/Rp = 3V/0.5Ω = 6A

Rotation physics corresponds to the rotational motion included in the kinematics. Rotation physics plays a major role in kinematics in explaining everything around starting from the rolling motion of a ball to the motion of planets in their respective orbits around the sun. Rotation physics mainly focuses on the study of rigid body motion such as rotation of a disc about a fixed axis, the motion of a solid sphere, the concept of torque, etc. Rotation physics gives a deep insight into the concept involved in rotation kinematics.

What is Called Rotation?

We observe the rotational motion in almost everything around us. Every machine, celestial bodies, most of the fun games in amusement parks, motion of the cricket ball, the way washing machines work, etc. The objects that turn about an axis exhibit rotational motion. All the particles and the centre of mass of the object do not undergo identical motions, but all the particles of the body undergo an identical motion. By definition, it becomes important for us to explore how the different particles of a rigid body move when the body is subjected to rotation.

In rotational kinematics, we will estimate the relation between kinematical parameters of rotation. Let us recall angular equivalents of the linear quantities: position, displacement, velocity, and acceleration which we usually consider during the study of an object that is subjected to circular motion. One should always remember that circular motion and rotational motion are two different aspects of physics and kinematics. 

Rolling is an example of this category. Arguably, the foremost important application of rotational physics is within the rolling of wheels and wheels like objects as our world is now crammed with automobiles and other rolling vehicles. The rolling motion of a body may be a combination of both translational and rotational motion of a round-shaped body placed on a surface. When a body is about during a rolling motion, every particle of the body has two velocities – one thanks to its rotational motion and therefore the other thanks to its translational motion (of the centre of mass), and therefore the resulting effect is that the resultant of both velocities in the least particles.

Rotation Definition Science

Let us try to understand what is called rotation physics and rotation definition science, what characterises rotation. You may notice that in the rotation of a rigid body about a fixed axis or fixed line, every particle of the body moves in a circle, which lies in a plane perpendicular to the axis and has its centre on the axis. The figure shown below illustrates the rotational motion of a rigid body.

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Now, consider few particles from a given object, let P₁ be a particle of the rigid body at a distance r₁from the fixed axis or the fixed-line. The particle executes a circle of the radius r₁ with a centre C₁ on the fixed-line. The circle lies in a plane perpendicular (or 90⁰) to the axis of rotation. From the figure, it shows that another particle P₂ of the rigid body, which is at a distance r₂ from the fixed axis or fixed-line. The particle P₂ describes a circle of the radius r₂ with a centre C₂ on the fixed axis. The circle described by the second particle also lies in a plane perpendicular to the fixed axis. We should notice that the circles described by P₁ and P₂ may lie in different planes, but both planes are perpendicular to the fixed axis. For any particle on the axis like P₃ , r = 0. Any such particle remains stationary while the body rotates. This is expected since the axis is fixed. 

In some illustrations of rotational motion, however, the axis may not be fixed. A prominent example of this kind of rotation is a spin top spinning in place, as shown in the given figure below. We assume that the spin top does not slip away from the place to place and so does not execute the translational motion. 

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Now, the axis of such a spinning top moves around the vertical axis through its point of contact with the ground, sweeping out a cone as shown in Figure. This movement of the axis of the spinning top around the vertical axis is known as the precession. The point of contact of the spin-top with the ground is fixed. The axis of rotation of the spin-top at any instant passes through the point of contact. 

Another simple illustration of this kind of rotational motion is the oscillating table fan or a pedestal fan where we see the rotation of wings of a fan about one fixed axis. The axis of rotation of such a table fan has an oscillating movement in a horizontal plane about the vertical axis through the point at which the axis is pivoted.

Now, in more general cases of rotational motion, such as the rotation of a spin-top or a pedestal fan, one point of the rigid body is fixed, not the one line. In this case, the axis of rotation will not be fixed, though it always passes through the fixed point. In rotation physics, however, we mostly deal with the simpler and special cases of rotational motion in which one line or the axis is fixed. Thus, the rotational motion will always be about a fixed axis or fixed-line. 

The rolling motion of a cylinder down an inclined plane is a combination of rotational motion about a fixed axis and translational motion. Thus, something else in the case of rolling motion which we referred to earlier is rotational motion.  So, according to the rotational motion meaning, the motion of a rigid body which is not pivoted or fixed in some way is either a pure translational motion or a combination of translational motion and rotational motion. The motion of a rigid body which is pivoted or fixed in some way is rotational motion. The rotational motion executed by any object is always about an axis that is fixed (e.g. a ceiling fan) or moving (e.g. an oscillating table fan). 

Did You Know?

• Rotation physics is an important part of classical mechanics. As the advancement took place the consideration of linear motion was getting contradicted. People were often confused with circular motion and rotational motion. After decades of understanding, physicists were able to conclude that rotational motion or rotation is the motion of a particle in a circular motion. 

• A two-dimensional object rotates about a centre (or point) of rotation. A three-dimensional object rotates
  about a line known as an axis. If the axis of rotation is within the body of the object, then the body is said to rotate upon itself, or spin, which refers to the relative speed and perhaps free-movement with angular momentum. A circular motion about an external point is known as an orbit or more precisely an orbital revolution, for example, the motion of the Earth around the Sun.

Schrodinger’s Equation refers to a fundamental equation of quantum physics. In classical physics, it is parallel to Newton’s Laws of Motion, which helps you to calculate the future position and momentum of the object if you know the present position and momentum of an object. Although parallel, Schrodinger’s Equation is not deterministic as Newton’s laws. Newton’s laws are deterministic because by using the given knowledge of the initial position and the measurements of the forces acting on the object, one can tell how the forces will interact, and therefore, where the object is going to be in the upcoming point of time. In 1925, Schrodinger and Heisenberg independently synthesized the representations of quantum mechanics that successfully describe physical phenomena at the microscopic level of nuclei, molecules, and atoms. Here, in the following article, we will discuss Schrodinger’s equation in deep.

Schrodinger’s Equation doesn’t tell the position of the subatomic particles at any future point in time. It will tell only the possible positions and probabilities of being in those possible positions. For instance, if you use a laser to shoot some photons towards a photographic plate, this equation can help you calculate the overall pattern of pixels that will form on the plate, but not the position of pixels the particular photon would light up. Hence, we can say that the Schrodinger’s Equation is deterministic but only at the statistical level, not at the individual particle level.

Another fact about Schrodinger’s Equation is that it is open to considerable interpretation and the nature of the physical reality that describes it.

The Schrodinger Equation comes up as a mathematical expression. It describes the transformation of the physical quantity overtime, where the quantum effects like a wave-particle duality. The equation has two forms, the time-independent Schrodinger equation and the time-dependent Schrodinger equation. 

The Time-Dependent Schrodinger Equation

De Broglie relation cannot be derived by using elementary methods although we are able to derive this equation starting from the classical wave equation. We can show that the time-dependent equation, if not derivable, is at least reasonable, and the arguments are rather involved.

Schrodinger Wave Equation Derivation (Time-Dependent)

The single-particle time-dependent Schrodinger equation is,

Where

V represents the potential energy and is assumed to be a real function

Now, if we write the wave function as a product of temporal and spatial terms, then the equation will become,

or

Since the right-hand side is a function of r only and the left-hand side is of t only, the two sides should equal a constant. In cases where we designate the constant E, the two ordinary differential equation, namely

and

Here, the former equation is solved to get,

However, the latter equation is the time-independent Schrödinger equation

Considering a complex plane wave:

Now the Hamiltonian of a system is

Where 

T is the kinetic energy and V is the potential energy. As we know that H is the total energy, we can rewrite the equation as:

Now, by taking the derivatives, we get

All of us know that,

Where 

‘λ’ is the wavelength 

‘k’ is the wave number.

Now, as we have

Hence,

Here,by multiplying the Hamiltonian to Ψ (x, t), we get,

The above expression can also be written as:

As the energy of a matter wave is

So, we can say that

Now, by combining the parts, we can get the Schrodinger Wave Equation.

So, this was the derivation of the Schrodinger Wave Equation (time-dependent)

Schrodinger Wave Equation Derivation (Time-Dependent)

How to extract the knowledge about momenta from Ψ(qj,t) is treated below, where the structure of quantum mechanics, the use of operators and wave functions to make predictions and interpretations about experimental measurements, and the origin of ‘uncertainty relations’ such as the well-known Heisenberg uncertainty condition dealing with measurements of coordinates and momenta are also treated.

Before moving deeper to understand what quantum mechanics actually ‘means,’ it is essential to learn how the wave functions ΨΨ are found by applying the basic equation of quantum mechanics, the Schrodinger equation, to a few exactly soluble model problems. Being aware of the solutions to these easy yet chemically relevant models will help you in being familiar with more details of the structure of quantum mechanics because these model cases can be used as ‘concrete examples.’

The Schrodinger equation is a differential equation based on all the spatial coordinates necessary to describe the system at hand and time (thirty-nine for the H2O example cited above). It is usually written as

HΨ=iℏ∂Ψ∂t(1.3.1)(1.3.1)HΨ=iℏ∂Ψ∂t

Where

Ψ(qjΨ(qj,t) is the unknown wave function 

H H is the operator corresponding to the total energy physical property of the system. This operator is called the Hamiltonian and is formed by first writing the classical mechanical expression for the total energy (potential + kinetic) in Cartesian coordinates and momenta and then replacing all the classical momenta ‘pj’ by the quantum mechanical operators pj=−iℏ∂∂qjpj=−iℏ∂∂qj. For H2O example mentioned above, the classical/mechanical energy of all the thirteen particles is

E=∑i(p2i2me+12∑je2ri,j−∑aZae2ri,a)+∑a(−ℏ22ma∂2∂q2a+12∑bZaZbe2ra,b)(1.3.2)(1.3.2)E=∑i(pi22me+12∑je2ri,j−∑aZae2ri,a)+∑a(−ℏ22ma∂2∂qa2+12∑bZaZbe2ra,b)

Where 

the indices i and j label the ten electrons whose thirty cartesian coordinates are {qii} 

the a and b label the three nuclei whose charges are represented by {Zaa}, and the nine cartesian coordinates are {qaa}. The electron and nuclear masses are denoted as me and {maa}, respectively.The corresponding Hamiltonian operator is

H=∑i(−(ℏ22me)∂2∂q2i+12∑je2ri,j−∑aZae2ri,a)+∑a(−(ℏ22ma)∂2∂q2a+12∑bZaZbe2ra,b).H=∑i(−(ℏ22me)∂2∂qi2+12∑je2ri,j−∑aZae2ri,a)+∑a(−(ℏ22ma)∂2∂qa2+12∑bZaZbe2ra,b).

Note that H is a second-order differential operator in the list of the thirty-nine Cartesian coordinates describing the positions of the three nuclei and ten electrons. The fact, which makes it a second-order operator, is that the quantum mechanical operator for every momentum p = iℏ∂∂qiℏ∂∂q is of the first order and momenta appear in the kinetic energy as p2jpj2 and p2apa2.

The Schrodinger equation for the H2O then reads

∑i[−(ℏ22me)∂2∂q2i+12∑je2ri,j−∑aZae2ri,a]Ψ+∑[−(ℏ22ma)∂2∂q2a+12∑bZaZbe2ra,b]Ψ∑i[−(ℏ22me)∂2∂qi2+12∑je2ri,j−∑aZae2ri,a]Ψ+∑[−(ℏ22ma)∂2∂qa2+12∑bZaZbe2ra,b]Ψ

=iℏ∂Ψ∂t=iℏ∂Ψ∂t

If the Hamiltonian operator contains the time variable explicitly, one must solve the time-dependent Schrödinger equation. If the Hamiltonian operator does not contain the time variable explicitly, one can solve the time-independent Schrodinger equation.

Schrodinger’s equation cannot be derived from anything. It is as fundamental and axiomatic in Quantum Mechanics as Newton’s Laws is in classical mechanics.On scrutinizing the definition, you will find that the relation H=T+V being used is nothing but the energy conservation principle. So, from a quantum viewpoint, Schrodinger’s equation is based on the energy conservation principle. Just as people have no proof for energy conservation except experiments that always appear to satisfy it, Schrodinger’s equation has no pen-and-paper proof. The only proof of its validity is experiments that have never violated the equation to date.

Introduction 

The building blocks of the electronic circuits are devices in which a controlled flow of electrons can be achieved. These devices were mostly vacuum tubes (also called valves) like the vacuum diode which had two electrodes, viz., anode (often called plate) and cathode; triode which has three electrodes – cathode, plate and grid; tetrode and pentode (respectively with 4 and 5 electrodes) in the 1940s and 1950s. These devices were high on weight, consumed a high amount of power, operated mostly at high voltages (100 V) and had limited life and low reliability. In the 1930s, the development of modern solid-state semiconductors was started. It was found that some solid state semiconductors and their junctions offered the possibility of controlling the number and the direction of flow of charge carriers through them. Simple excitations like light, heat or small applied voltage can change the number of mobile charges in a semiconductor and flow of charge carriers in the semiconductor devices are within the solid itself.

In case of semiconductor devices, no external heating or large evacuated space is required. Semiconductor electronics are smaller in size, consume less power, operate at lower voltages and have long life and high reliability. Students have Semiconductor class 12 chapter in Physics, they can go through this article to understand in a simplified manner.

Semiconductor Material 

If a material has an electrical conductivity between that of a conductor and an insulator, it can be classified as a semiconductor material. Its resistance decreases as its temperature rises while the metals are the opposite. Its conducting properties can be changed by introducing impurities or doping into the crystal structure. When two differently-doped parts are present in the same crystal, a semiconductor junction is created. Silicon, germanium, gallium arsenide, and elements near the so-called “metalloid staircase” on the periodic table are some of the examples of semiconductor materials. 

Silicon is the most commonly used material in the devices and also it is the most critical element to fabricate the electronic circuits. Gallium arsenide is the most common semiconductor after Silicon and is used in laser diodes, solar cells, microwave-frequency integrated circuits and others. By addition of a small amount (of the order of 1 in 108) of pentavalent (antimony, phosphorus, or arsenic) or trivalent (boron, gallium, indium) atoms, conductivity of silicon is increased. This process is called doping and the resultant semiconductors are known as doped or extrinsic semiconductors. The conductivity of a semiconductor can equally be improved by increasing its temperature apart from doping.

Doping process highly increases the number of charge carriers within the crystal. If a doped semiconductor material contains more free holes it is called “p-type”, and when it contains more free electrons it is known as “n-type”.

N-type (e.g. Doped with Antimony)

 In N-type semiconductors the characteristics are as follows:

1. The Donors are positively charged.

2. A large number of free electrons.

3. A small number of holes in relation to the number of free electrons.

4. Doping gives positively charged donors and negatively charged free electrons.

5. Supply of energy gives negatively charged free electrons and positively charged holes.

P-type (e.g. Doped with Boron) 

In these, types of materials have characteristics as follows:

1. The Acceptors are negatively charged.

2. There are a large number of holes.

3. A small number of free electrons in relation to the number of holes.

4. Doping gives negatively charged acceptors and-positively charged holes.

5. Supply of energy gives positively charged holes and negatively charged free electrons.

Intrinsic or Pure Semiconductors

Un-doped semiconductors are called intrinsic or pure semiconductors. There are no dopant species present. The number of charge carriers is determined by properties of the material itself and not by the amount of impurities. Number of excited electrons and number of holes are in equal amounts i.e. n=p. There can be electrical conductivity in intrinsic semiconductors and it can be due to crystallographic defects or electron excitation. A silicon crystal is not like an insulator. At a temperature above zero, there is a chance that an electron in the lattice will be removed from its position, leaving behind an electron deficiency called a “hole”. At that stage, when a voltage is applied, then both the electron and the hole can contribute to a small current flow.

Types of Semiconductor Devices

• These devices are differentiated into two-terminal or three- terminal devices and sometimes for terminal devices. The examples of two-terminal devices include Diode, Zener diode, Laser diode, Schottky diode, Light-emitting diode (LED), Photocell, Phototransistor, Solar cell, etc.

• Some of the examples of three terminal semiconductor devices include bipolar transistor, IGBT, Field-effect transistor, Silicon-controlled rectifier, TRIAC, Thyristor, etc.

Diode

A diode is a semiconductor device that comprises a single p-n junction. P-n junctions are usually formed by joining up of p-type and n-type semiconductor materials. This formation is due to the reason that n-type region has the higher number of electron concentrations whereas the p-type region has a higher number of hole concentration, hence, the electrons get diffused from the n-type region to the p-type region. Hence, this phenomenon is used in generating light.

Transistors

Transistors are of two types: bipolar junction transistor and field effect transistor. The bipolar junction transistor is achieved by the formation of two p-n junctions in two different configurations like n-p-n or p-n-p.

The field effect transistor works on the principle of conductivity and the conductivity can be altered by the presence of an electric field.

We can understand sliding friction as the resistance force created between any two bodies when sliding against each other. This friction is also called kinetic friction and it is defined as the force that is required to keep a surface sliding along another surface. It hangs on two variables- one is material or the thing and the other is the weight and size of the object. Any variation in the surface area in contact does not change the sliding friction. In most materials, sliding friction is much less than static friction.

                         

                                          Image: Sliding Friction

Sliding can occur among two objects of random shape, whereas rolling friction is the frictional force related to the rotational movement of a somewhat disc-like or any other circular object along a surface. Usually, the frictional force of rolling friction is much less than that related to sliding kinetic friction. Usual values for the coefficient of rolling friction are smaller than that of sliding friction. Similarly, sliding friction usually produces more sound and more thermal bi-products. 

One example is braking motor vehicle tires on a roadway, a process that generates considerable heat and sound, and is taken into account in measuring the magnitude of roadway noise pollution. We can take a simple example when we stop our car at a stop sign then it slows down due to friction between applied breaks and the wheels. Thus, the force which is acted in the opposite direction where a body wants to slide is called sliding friction Some key categories of friction are rolling, sliding, static, fluid friction. Here we will discuss sliding friction or kinetic friction, it’s coefficient through which it is measured, and its examples.

Sliding Friction Definition

The frictional force which resists the real relative sliding motion between two contact surfaces is known as sliding or kinetic friction. Let us begin by studying frictional forces from simple understanding. Suppose there is a metal block on a table, a weak force may not set the metal block into motion. As you keep increasing the force progressively, with a particular amount of force, the metal block starts moving. The controlling value of the force at which the metal block starts moving is the same as the resistive force offered by the metal block under the static form. Hence that resistive force is called Static Friction. Ongoing the experiment, increasing the force further, makes the metal block move. But even after the metal block started moving, it still provides a resistive force trying to oppose the motion. It is defined as the ‘sliding friction’. From what we termed so far, it is clear that the sliding friction is smaller than the static friction.

The force of sliding friction is directly proportional to the weight, acting in the direction normal to the surface. As a specific case, if the surface on which the body slides is horizontal, then the normal force matches the weight of the object.

  

Sliding Friction Formula

The equation for sliding force contains the coefficient of sliding friction times the normal force.

F[_{s}] = [mu _{s}] [F_{n}]

Where,

F[_{s}] = force of sliding friction

[mu _{s}] = Coefficient of sliding friction

[F_{n}] = normal force

Motion under Sliding Friction

The motion under sliding friction can be shown (in simple systems of motion) by Newton’s Second Law

∑ F= ma 

[F_{E}] – [F_{K}] = ma

Where [F_{E}] is an external force.

• Acceleration happens when the outside force is greater than the force of kinetic friction.

• Slowing Down (Or Stopping) happens when the force of kinetic friction is bigger than that of the outside force.

• This is also followed by Newton’s first law of motion as there exists a net force on the object.

• Constant Velocity happens when there is no net force on the object, that is the outside force is equal to the force of kinetic friction

Motion on an Inclined Plane

A block can be used to understand friction as it slides up or down an inclined plane. This is shown in the free body diagram below

The component of the force of gravity in the direction of the incline is shown by:

[F_{g}] = mg sin

The normal force (perpendicular to the surface) is shown by.

N= mg  cos

Therefore, since the force of friction resists the motion of the block

[F_{k}] = [mu _{k}] · mg cos

To find the coefficient of kinetic friction on an inclined plane, one must see that the moment where the force is parallel to the plane is the same as the force perpendicular; this occurs when the object is moving at a constant velocity at some angle  

[F_{g}] = mg sin

∑ F = ma =0 

[F_{k}] = [F_{g}] or = [mu _{k}] · mg cos= mg sin

 [mu _{k}] = tan

Understanding Sliding Friction

Sliding friction produced or generated by objects is said as a coefficient that takes into consideration of several factors that can affect the level of friction. These several factors that can impact sliding friction include the following:

• The surface distortion of objects.

• The roughness or smoothness of the surface.

• The original velocity of either object.

• The size and shape of the object.

• The amount of pressure on any object.

• The adhesion force of the surface.

Sliding Friction Characteristics

We have already explained before that in general, sliding friction is always smaller than static friction for the same set of the body and the surface movement. This also leads to another conclusion that the frictional force always depends on the nature of the material of the object and surface. As also explained in the past, a sliding force is proportional to the normal force, which means the load of the object. In the experimentation, we had clarified in the previous section the amount of the sliding friction will be equal even when you change the side of the block that rests on the table. Hence, for the equal mass, the sliding friction is free of the area of contact. The sliding friction is also independent of the speed of motion.

The coefficient of Sliding Friction

We have given an overall definition that a frictional force F seen by an object is directly proportional to the normal force N exerted by that. That is,

F=μNF

Where µ is a constant it is called the coefficient of friction. It is clearly a ratio of two forces and therefore it has no dimensions. If the friction is static, then the coefficient of friction is named as ‘coefficient of static friction and denoted by μs and for sliding friction the same constant is known as ‘coefficient of sliding friction and is denoted by μk. The subscript ‘k’ is used to mean ‘kinetic’. Then sliding friction is always smaller than static friction and so,  [mu _{k}] < [mu _{s}].

Sliding Friction Examples

There are no various examples of sliding friction as the degree of sliding friction is extensive. The sliding friction between two surfaces produces heat due to molecular interactions. The amount of heat produced depends on the materials of the surfaces and might turn into a fire sometimes. Lighting a match stick is an extraordinary example in present-day life. Stone age men used two stones for ignition.  Because of a high degree of frictional force in sliding friction, one favours to put an object on the wheel and transport instead of pushing along because of the fact that the result of rolling friction is far smaller than that of sliding friction. The values for the coefficient of rolling friction are quite smaller than that of sliding friction.

Imagine a car parked on an inclined plane with less gradient. In the absence of sliding friction, the wheels of the car will begin to rotate and start moving. This is the reason, at steep gradients, hand brakes are used while parking and in worst cases, heavy stones are placed behind the tires. Sliding friction, because of a considerable level, in a way is helpful in real life.

A few examples like sliding friction

• Pushing a heavy and bigger object such as a crowbar 

• Ribbing a weight on ramps

The article discusses all the necessary information related to sliding friction such as its definition, formula and motion on different types of surfaces and characteristics of sliding friction etc.

Solid state detector, is also known as Semiconductor Radiation Detector. The discovery of semiconductors and the invention of the transistor in 1947 has an impact on Electronics, Computer Technology, telecommunications, and Instrumentation. The materials can be classified as conductors, semiconductors, and insulators on the basis of their conductivity. Semiconductors include the materials having conductivity lying between the conductivity of conductors and that of insulators.

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A radiation detector in which the detecting medium is a solid state detector (semiconductor) material such as a silicon or germanium crystal. The solid state detector has conductivity in the range 104 to 10-6 Sm-1. As a beam of ionizing radiation passes through the device, it creates a p-n junction, which generates a current pulse. In a different device, the absorption of ionizing radiation generates pairs of charge carriers (current carries or electrons called holes) in a block of semiconducting material. The pulses created in this way are recorded, amplified, and analyzed to examine the energy, number, or identity of the incident charged particles. The sensitivity of solid state detectors can be improved by running them at low temperatures, such as 164°C (263°F), which suppresses the spontaneous forming of charge carriers due to thermal vibration. A semiconductor radiation detector in which a semiconductor material such as a silicon or germanium crystal constitutes the detecting medium. 

The Intrinsic and Extrinsic Solid State Detector

Intrinsic Semiconductor

An extremely pure solid state detector is called an intrinsic semiconductor. An example of intrinsic semiconductors is silicon, germanium. Si (silicon) atom has 4 valence electrons. Silicon atoms share their four valence electrons with their four neighbour atoms and also take a share of 1 electron from each neighbour.  At absolute zero temperature, the valence electron band is filled and the conduction band is empty. The departure of an electron from a valence bond creates a vacancy in the bond that is called a hole. That is, every thermally separated bond creates electron-hole pair. In intrinsic semiconductor total current is the sum of electronic current I_e and the hole current is I_h. Here the formula is, I = I_e + I_h.

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Extrinsic Semiconductor

The conductivity of an intrinsic semiconductor can permanently be increased, by adding suitable impurities. Hence the process of adding impurity to pure semiconductors called doping and the impurity atoms are called dopants. A doped solid state detector is called an extrinsic semiconductor. The Dopant atom should not distort the original semiconductor crystal structure.

Solid State Nuclear Track Detector

A solid state nuclear track detector (also known as a dielectric track detector, DTD) is a sample of a solid material (crystal, photographic emulsion, glass or plastic) exposed to a nuclear track detector (neutrons or charged particles), etched, and examined microscopically. Solid state nuclear track detector particles have a higher etching rate than bulk material and the shape and size of these tracks yield information about the charge, mass, energy and direction of motion of the particles. The precise knowledge available on individual particles is one of the key benefits over other solid state radiation detectors, the persistence of the tracks allowing measurements to be made over long periods of solid, and the simple, and robust construction of the detector. 

Types of Semiconductor Detectors

There are Two Types of Detectors are as Follows,

1. N-Type Detectors

2. P-Type Detectors

N-Type Detector

The solid detector has a large number of electrons in the conduction band and the conductivity is due to negatively charged electrons it is called an n-type solid detector. The n-type semiconductor also has a few electrons and holes produced because of thermally broken bonds. Though n-type detectors have a large number of electrons, its net charge is neutral (zero). When Si or Ge crystals are doped with a pentavalent impurity such as Arsenic(As), Phosphorus (P), Antimony (Sb), we get an n-type semiconductor.

Therefore, valence orbit can hold a maximum of eight electrons, the fifth (extra) electron of the dopant atom is not part of covalent bonding and hence it is loosely bound with its core. Small energy is required to break the bound. It is 0.05 eV for Silicon and 0.01 eV for Germanium.

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P-Type Detector

The solid detector has a large number of holes and conductivity is because of positively charged holes, it is called a p-type semiconductor. The p-type solid detector has a large number of holes created by trivalent dopants and few electron-hole pairs because of thermally broken bonds. Though the p-types detector has a large number of holes, its net charge is neutral (zero). The p-type of detector has holes as majority carriers and electrons as minority carriers. When Si or Ge crystals are doped with trivalent impurities such as boron (B), aluminium (Al), indium (In), we get a p-type semiconductor. This trivalent atom has three electrons in a valence orbit.  

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The Solid State Radiation Detector

The process which occurs during the detection of nuclear radiation in a solid-state device is considered in brief, and the advantages of the reverse-biased semiconductor junction in germanium or silicon are set out. The effects of radiation damage, as well as the factors that determine a detector’s energy resolution, are investigated. The preparation of detectors is not discussed in detail, but the physical concepts on which the various types of detectors are based are briefly mentioned. The terminating section surveys the field of applications of solid state detectors in nuclear physics, radiochemical analysis, space research, medicine and biology. In the medical field, it is used as a solid state x-ray detector.

Solid state photomultipliers are called Silicon photomultipliers, often denoted  “SiPM” in the literature. Although the device works in switching mode, most solid state photomultiplier (SiPM) is an analogue device because all the microcells are read in parallel and making it possible to generate signals within a dynamic range from 1 photon to 1000 photons for a device with just a square millimetre area.

Fun Facts

1. The solid detector is very small in size and light in weight.

2. They do not have a heating element and hence low power consumption. 

3. Detectors do not have warm up time.

4. They can operate on low voltage.

5. The solid detector is used in the medical field also as a solid state x-ray detector.

6. They have a high speed of operations. 

7. A complementary device is possible such as n-p-n and p-n-p transistors.