Category: Physics Notes PPT

Put some drops of water on one side on a slanting surface and some drops of honey on the other. Come back and observe the flow of both the liquids. You would note that the slowness of water was very quick whereas honey was not that easily movable. In this case, honey is considered to be Viscous. 

So, viscosity is defined as the ratio of the force required to make adjacent layers of the liquid move over each other.

Figure .1 (a) shows an ideal or superfluid with no friction however, practically there is always some friction in the fluids as shown in the figure. 1(b).

Let’s take an example,

As you can see in the figure.2 above, there is a variation in each horizontal layer of the liquid that is happening due to the presence of some internal friction (viscosity) between the layers of the fluid passing via two plates.

The concept has significant importance for competitive exams like JEE and NEET. So the faculty at has holistically covered the topic keeping in mind the need of every student. So in this article, we shall be learning about – 

Table of Content

• Introduction

• What is the viscous gradient?

• What is the Coefficient of Viscosity?

• SI Unit of Coefficient of Viscosity

• Unit of Coefficient of Viscosity

• Coefficient of Viscosity Unit and Dimension

• The viscosity of Water in SI Units

• Do You Know?

• Benefits of studying with  

• Frequently asked questions

What is a Viscous Gradient?

The viscous gradient is the difference in the velocity between the adjacent layer of the fluid. If more force is applied by the upper layer to move forward the more will be the viscous gradient. It is represented by v/x, where v is the velocity difference and x will be the difference of distance between the two layers. So, the higher the value of v/x, the more will be the viscous gradient. 

Coefficient of Viscosity

The ratio of the shearing stress to the velocity gradient of the fluid is called the coefficient of viscosity η.

Hence the coefficient of viscosity is given by,

         

η  = F . d / A .ⅴ

Where F is the tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

ⅴ is the velocity.

A is the area

d is the distance between the two layers of liquid skidding over each other.

The difference in the stream of velocity between the adjacent layers of the fluid is measured in the velocity gradient.

The viscosity of gas is less than the liquid viscosity.

SI Unit of Coefficient of Viscosity

Every liquid has its specific viscosity and the measure of this attribute is called the coefficient of viscosity.

The coefficient of viscosity η is defined as the tangential force F required to maintain a unit velocity gradient between two parallel layers of liquid of unit area A.

The SI unit of η is Newton-second per square meter (Ns. m^-2) or

Pascal-seconds (Pa .s)

Hence the coefficient of viscosity is a measure of the resistance of the fluid to deformation at a given rate due to internal friction.

Unit of Coefficient of Viscosity

The centimetre-gram-second or CGS unit of coefficient of viscosity,  η is 

dyne-sec/ cm² which is equal to Poise.

Where one poise is exactly 0.1 Pa·s.

The meter-kilogram-second or MKS unit is: Kilogram per meter per second or

Kg m^-1 s^-1.

Coefficient of Viscosity Unit and Dimension

Since, the formula for coefficient of viscosity is given by,

η  = F . d/ A .ⅴ  =  MLT⁻² . L / L² . LT ⁻¹

On solving  we get,

The Viscosity of Water in SI Units

The coefficient of viscosity of water can be determined by using Poiseuille’s law.

Poiseuille’s equation for the flow of liquid determines the volume of the liquid flowing through a capillary tube in a unit of time.

Poiseuille’s formula is given by,

Here, the rate of flow of the viscous liquid through a tube of length ‘l’ and radius ‘໗’ is proportional to the applied pressure P. 

The rate of flow of the viscous liquid is proportional to the fourth power of the inner radius of the tube and inversely proportional to the viscosity of the liquid and the length of the tube. 

The formula for the coefficient of viscosity of water is given by,

Here, Ⅴ  is the rate of flow of the volume of liquid.

P is the pressure that would be applied to the liquid.

໗ is the inner radius of the capillary tube.

l is the length of the capillary tube.

SI unit of viscosity of water is Ns.m^-2 or Pa.s.

Do You know?

The dynamic viscosity of water at room temperature  25⁰C are having various values mentioned below:

In the SI unit, the value of viscosity is 8.90 × 10^{– 4} Pa·s.

In CGS unit, the value of viscosity is 8.
90 × 10^{– 3} dyn·s/cm² or  0.890 cP.

Therefore, water has a viscosity of 0.0091 poise

Viscosity and density are two different terms where viscosity is the thickness of fluid and density refers to the space between its particles.

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A mirror can be termed as a highly polished and smooth reflecting surface. The most common types of mirrors that are used are plane mirrors. The spherical mirror is part of the spherical reflecting surface. There are two categories of spherical mirrors – concave mirrors and convex mirrors.

Concave mirror: 

Concave mirror has a reflecting surface that caves inwards. The concave mirrors essentially converge light to only one prime focus point. This is why they are also known as converging mirrors. These mirrors are used for focusing light and the image that is formed by the concave mirror differs in size based on object position with respect to the mirror. The image exists either in virtual or real form. Erect or magnified and inverted, of the same size as that of the object or diminished, and it all depends on the position of the object. 

Convex mirror: 

The convex mirror is the curved mirror where the reflective surface bulges out towards the position of the light source. The convex mirrors tend to reflect light in the outwards direction, diverging light rays, and hence they are not used for focusing light. The image is erect, virtual, and smaller than the object, however gets larger as the object comes closer to the mirror. These mirrors are also referred to as diverging mirrors. 

Mirrors and the reflection laws

When we have a look at ourselves in the flat mirror, we appear to be of the same size as we actually are and our distance appears to be as behind the mirror as we actually are standing in front of the mirror. This is due to how reflection happens and it is known as the laws of reflection. According to the 1st law of reflection, the light, which hits a mirror would essentially bounce back at the same angle. If the specific mirror is flat, then it would lead to the image appearing as life-size. The image type that is created by the flat mirror, is known as the virtual image since it appears behind the mirror. The reflection laws are valid and hold true for any type of surface or mirror. 

The different terms that are used in spherical mirrors are pole, a centre of curvature, a radius of curvature, principal axis, aperture, focus, focal length. The pole is the midpoint of the mirror while the centre of curvature is the centre of the sphere, which is part of the image formed by the mirror. The radius of curvature refers to the distance between the centre of curvature and the pole. Its focal length is twice the length of the mirror. 

The principal axis is essentially the imaginary line that passes via the pole and centre of curvature of a spherical mirror. Aperture is used for denoting the mirror size. The focus is the point on the principal axis, where light rays that are parallel to the principal axis will appear to diverge from (for convex mirror) or converge ( for concave mirror) after reflecting from the mirror. The focal length is the distance between the focus of the mirror and the pole.

More on the Topic

A mirror is a part of a smooth and highly polished reflecting surface. Most commonly used mirrors are plane mirrors. A spherical mirror is a part of a spherical reflecting surface. There are two types of spherical mirrors – convex mirror and concave mirror.

Convex Mirror:

Convex mirror is a curved mirror for which the reflective surface bulges out towards the light source. Convex mirrors reflect light outwards (diverging light rays) and therefore they are not used to focus light. The image is virtual, erect and smaller in size than the object, but gets larger (maximum upto the size of the object) as the object comes towards the mirror. Such mirrors are also called diverging mirrors.

Concave Mirror:

A concave mirror has the reflecting surface that caves inwards. Concave mirrors converge light to one prime focus point. Therefore, they are also called converging mirrors. They are used to focus light. The image formed by a concave mirror varies in size depending on the position of the object with respect to the mirror. The image can be real or virtual, erect or inverted and magnified, diminished or of the same size as that of the object, all depending on the position of the object.

 

Real images can be brought onto a screen and they are always inverted.

Mirrors and reflection Laws of Reflection:

When we look at ourselves in a flat mirror, we will appear in the same size as we are and will appear to be just as far behind the mirror as we will be actually standing in front of the mirror.

This is because of how reflection takes place. This is concluded as the laws of reflection. The first law of reflection says that the light that hits a mirror would bounce back at the same angle. If the mirror is flat that would cause the image to appear life-size. 

The type of image created by a flat mirror is called the virtual image as it will appear behind the mirror. 

Laws of reflection are valid for any type or mirror or surface. 

Terms Used in Spherical Mirrors:

• Pole (P): It is the midpoint of a mirror.

• Centre of Curvature (C): It is the centre of the sphere of which the mirror forms a part.

• The Radius of Curvature (R): It is the distance between the pole and the centre of the curvature. It is twice the focal length of the mirror.

• Principal Axis: An imaginary line that is passing through the pole and the centre of curvature of the spherical mirror.

• Aperture: It is used to denote the size of the mirror.

• Focus: It is the point on the principal axis, where the light rays parallel to the principal axis will converge (in the case of a concave mirror) or appear to diverge from (in the case of a convex mirror) after reflection from the mirror.

• Focal Length: The distance between the pole and the focus of the mirror.

Properties of the Images Formed by a Convex Mirror:

Whatever be the position of the object in front of the convex mirror, the images is always smaller than the object, erect, virtual and also formed within the focus. 

Why is that a Convex Mirror Never Forms a Real Image?

A real image occurs where rays converge, whereas virtual image occurs when rays diverge and only appear to come from a point. The real images cannot be produced by a convex mirror as it diverges the rays. 

Real Image:

The real image is formed as a result of the actual convergence of the reflected light rays. It can be received on a screen and it is always inverted.

Do Concave Mirrors Always Form Real Images?

The concave mirror forms an image and that depends on the two parameters: the object distance and the focal length of the mirror.

If the object is placed between the pole and the focus of a concave mirror, a magnified and erect virtual is found to be formed.

Difference Between Convex and Concave Mirrors:

Image Formation by Concave and Convex Mirrors:

Convex Mirror Ray Diagram:

• When an object is placed at a finite distance from the mirror, the virtual image will be formed between the pole and focus. The size of the image is smaller as compared to the object.

Concave Mirror Ray Diagram:

• A real image will be formed between the focus and centre of curvature, when the object is placed beyond the centre of curvature. The size will be small as compared to the object.

• When an object or thing is set at the centre of curvature, the real image gets formed at the centre of the curvature. The size of the image is the same as that of the object.

• When an object/thing is set between the curvature and focus, the real image will be formed beyond the centre of curvature. The size will be larger as compared to the object.

• When an object is placed at the focus, the real image will be formed at infinity. The size of the image is much larger as compared to the object that is placed at the focus.

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Uses of Convex Mirrors:

The convex mirror is used as a side-view/rear – view mirror of a vehicle because it forms an erect and smaller image. Convex mirror gives a wide rear view.

The convex mirror is suitable for convenient shops and big supermarkets and any other corner for a wide observation.

They can be used as street light reflectors because they can spread the light over a bigger area.

They are put on the corners of roads so that the drivers can see any vehicles and avoid collisions by taking due measures.

Uses of Concave Mirrors:

The concave mirror is a converging mirror, so it is used for many purposes. 

• It is used in a torch, automobile headlamps, lighthouses etc to reflect the light and make a fine beam.

• It is used in the aircraft landing at the airports to guide the airplane.

• It is used in the shaving process where you can get an enlarged and erect image of the face.

• It is used in solar ovens also. It collects a large amount of solar energy and focuses to a point where the vessel containing water or item to be cooked is placed.

• Concave mirrors are used in satellite dishes, they are also used by dentists and ENT doctors use them to obtain a larger image.

• Concave mirrors are used in electronic microscope, astronomical telescopes, visual bomb detectors etc.

A continuity equation becomes useful if a flux can be defined. To explain flux, first, there must be a quantity q that can flow or move, such as energy, mass, electric charge, momentum, number of molecules, etc. Let us assume ρ is the volume density of this quantity (q), that is, the amount of q per unit volume.

The way by which this quantity q is flowing is described by its flux.

In Continuity Equation, Flux is of Two Types:

• Volumetric Flux – Across a unit area, the rate of volume flow is known as Volumetric flux. It is calculated by the formula Volumetric flux =liters/(second*area). Its SI unit is ([ m^ {3} s^ {-1} m^ {-2} ])

• Mass Flux – It is the rate of mass flow. Its SI unit is (kg [ m^{-2}s^{-1} ]). It is represented by the symbols j, J, Q, q.

What is the Continuity Equation?

The continuity equation is an equation that describes the transport of some quantities like fluid or gas. It is also known as the transport equation. The continuity equation is very simple and powerful when it is applied to a conserved quantity. When it is applied to an extensive quantity it can be generalized. Physical phenomena are conserved using continuity equations like energy, mass, momentum, natural quantities, and electric charge.

According to the continuity equation:

[ A_{1} V_{1} = A_{2} V_{2} ]

Where,

[A_{1}] = cross-sectional area of region 1

[V_{1}] = flow velocity in region 1

[A_{2}] = cross-sectional area of region 2

[V_{2}] = flow velocity in region 2.

Continuity equations are a local and stronger form of conservation laws. For example, a weak version of the law of conservation of energy states that energy can neither be created nor destroyed which means that the total amount of energy in the universe is fixed. It means energy can neither be created nor destroyed nor can it teleport from one place to another—it can only move by continuous flow. 

A continuity equation is nothing but a mathematical way to explain this kind of statement. The continuity equation consists of many other transport equations like the convection-diffusion equation, Navier–Stokes equations, and the Boltzmann transport equation. 

• Convection–Diffusion Equation – It is a combination of convection and diffusion equations. It describes the physical phenomena where particles, energy, and other physical quantities are transferred with the help of ‘diffusion and convection’ inside a physical system.

• Boltzmann Transport Equation – Boltzmann transport equation describes the behavior (statistical in nature) of the thermodynamic system, which is not in the state of rest or equilibrium. 

Continuity Principle 

Continuity principle refers to the principle of fluid mechanics. The principle of continuity equation is a consequence of the law of conservation of mass. Through the continuity equation, the behavior of fluid is described when it is in motion. Whereas, the second equation is based on Newton’s law of motion (which describes the motion of an object and the force acting on its flow) and the third equation is based on ‘the law of conservation of energy (which states that mass can be neither created nor destroyed.)

Integral Form

The integral form of the continuity equation says that:

In terms of mathematics, the integral form of the continuity equation expressing the rate of increase of q within a volume V is:

[ frac{dq}{dt} + ∯ S j . dS = sum ]

• Here, S  denotes an imaginary closed surface, that encloses a volume V,

Flow Rate Formula

This equation gives very useful information about the flow of liquids and their behavior when it flows in a pipe or hose. The hose, a flexible tube, whose diameter decreases along its length has a direct consequence. The volume of water flowing through the hose must be equal to the flow rate on the other end. The flow rate of a liquid means how much a liquid passes through an area in a given time.

The formula for the flow rate is given below- 

The Equation of Continuity can be written as:

m = [ rho_{i1} v_{i1}A_{i1} + rho_{i2} v_{i2} A_{i2} +…..+ rho _{in} v_{in} A_{in} ]

m=[ rho_{01} v_{01} A_{01} + rho_{02} v_{02} A_{02} + ….+ rho_{0n} v_{0n} A_{0n} ] ……….. (1)

Where,

m = Mass flow rate

[rho] = Density

v = Speed

A = Area

With uniform density equation (1) it can be modified further –

q = [ v_{i1} A_{i1} + v_{i2} A_{i2} +….+ v{_im} A_{im} ]

q = [ v_{01} A_{01} + v_{02} A_{02} +….+V_{0m} A_{0m} ]

Where,

q = Flow rate

[ rho_{i1} =rho_{i2}.. = rho_{in} = rho_{01} = rho_{02}= …. = rho_{0m}]

Fluid Dynamics

The continuity equation in fluid dynamics says that in any steady-state process, the rate at which mass leaves the system is equal to the rate at which mass enters a system including the accumulation of mass within the system.

The differential form of the continuity equation is:

∂ρ∂t + ▽⋅(ρu)=0

Where,

t = Time

[rho] = Fluid density

u = Flow velocity vector field.

The derivative time can be understood as the loss of mass in accumulation inside the system, while the divergence term means the difference in flow in and flow out. The above-mentioned equation is also one of the (fluid dynamics) Euler equations. The equations of Navier–Stokes form a vector continuity equation expressing the conservation of linear momentum.

Uses of the Continuity Equation

The continuity equation is commonly used in pipes, tubes, and ducts. These structures have flowing fluid or gasses etc. which need a specific flow to be moved. Continuity equation can also be applied to huge water sources such as rivers, lakes, etc. This equation can also be applied in diaries, power plants, road logistics, etc. 

Along with this, the modern application of continuity equations includes computer networking and semiconductor technologies, etc. which uses a specific path to move data from one location to another. It is also used in gas pipelines and underground connections to transport gas. 

Continuity Equation Example

1. If 10 m³/h of water flows through a 100 mm inside diameter pipe. If the inside diameter of the pipe is reduced to 80 mm. Calculate the velocities.

Solution) Velocity of 100 mm pipe:

Putting the equation (2), to calculate the velocity of 100 mm pipe

(10 m³/h)(1/3600 h/s)=v100 (3.14(0.1 m) 2/4)

or,

v100= (10 m³/h) (1/3600 h/s) (3.14(0.1)2/4)

=0.35 m/s

Velocity of 80 mm pipe:

Again applying equation (2), to calculate the velocity of 80 mm p
ipe

(10 m³/h)(1/3600 h/s)= v80 (3.14(0.08 m) 2/4)

or,

v80= (10 m³/h) (1/3600 h/s) (3.14(0.08 m)2/4)

=0.55 m/s.

Astronomy is derived from the Greek word ‘ἀστρονομία’, where ἀστρον or Astron means ‘star’ and νομία or nomia from νόμος (nomia), which literally means the law or culture of stars.

It is a science that studies the laws of the stars, i.e., everything outside the Earth’s atmosphere.

Cosmology is derived from the Greek word κόσμος, where kosmos mean “world” and -λογία, or -logia means “study of”).

For studying the science behind the origination and development of the universe, we use the term ‘cosmology’. However, cosmology is a branch of astronomy that studies the Universe as a whole.

Cosmology Astronomy 

This page will provide the introduction to astronomy and cosmology, cosmology astronomy, basic astronomy and cosmology, astronomy astrophysics cosmology, and extragalactic astronomy and cosmology in detail.

Now, let’s understand astronomy and cosmology in detail:

Cosmology 

In 1656, the term cosmology was first employed in an English dictionary named Thomas Blount’s Glossographia.

In the year 1731, the term ‘cosmology’ was carried to in Latin by a German philosopher named Christian Wolff, in Cosmologia Generalis.

Cosmology is focused on studying the origin and evolution of the universe, from the Big Bang to today and on into the future. It applies a scientific approach to study the origin, evolution, and eventual dismissal of the universe. 

One of the types of cosmology is Physical cosmology. It is the scientific study of the origin of the universe, its large-scale structures and dynamics, and its ultimate dismissal, as well as the laws of science that govern the areas mentioned above.

Astronomy

All the celestial objects residing in space have their significance and to study these, we use the term ‘astronomy’.We use astronomy word as terminology to study the science of celestial objects, space, and the physical universe. 

It is one of the oldest natural sciences that studies celestial objects and their processes. The objects may include all the planets, moons, stars, galaxies, nebulae, and comets. 

Astronomy uses mathematics, physics, and chemistry to explain their origin and evolution.

Astronomy allows astronomers to study various ongoing spatial phenomena, and these are as follows:

Supernova explosions, 

Gamma-ray bursts, 

Quasars, 

Blazars, 

Pulsars, and 

Cosmic microwave background radiation. More specifically, astronomy studies everything that originates outside the Earth’s region.

However, cosmology is a term that takes into account the theory behind the building of the universe and modern cosmology is the next step after the Big Bang Theory.

Astrophysics Astronomy Cosmology

The ancient period recorded history made methodical observations of the dark sky; these include the following:

• Babylonians

• Greeks

• Indians

• Chinese

• Egyptians

Maya, and many more ancient diligent Americans.

In the ancient period, astronomy involved various disciplines like celestial navigation, astrometry, observational astronomy, and the preparation of calendars. Nowadays, professional astronomy is said to be akin to astrophysics.

Professional astronomy is divided into two branches, viz: observational and theoretical. 

Observational astronomy focuses primarily on gathering data by observing astronomical or celestial objects and this data is then analyzed by using basic astronomy and cosmology principles of Physics. 

However, theoretical astronomy is centred on the development of computer or analytical models to study and describe astronomical objects and their phenomena. These two fields complement each other. This part tries to explain observational results and observations are used to affirm our theoretical results.

So, basic astronomy and cosmology talk about the things mentioned above. 

Astrophysics Astronomy Cosmology

“Astrophysics” and “Astronomy” are synonyms to each other. According to the dictionary definitions, “astrophysics” refers to the branch of astronomy that deals with “the behaviour, physical properties, and dynamic processes of celestial objects and phenomena, while “astronomy” is “the study of all the around the Earth’s region and the study of their physical and chemical properties using Physics, Chemistry, and Mathematics. 

Extragalactic Astronomy and Cosmology

Extragalactic Astronomy and Cosmology is a book written by Peter Schneider. This book is very useful for Aeronautical Engineering students and also for those who have an interest in developing their knowledge in the field of Spacecraft and Space Engineering.

Observational Astronomy

Visible light is the main source of information about celestial bodies and their processes, or more specifically the electromagnetic radiation. 

Observational astronomy can be subdivided into fields according to the corresponding region of the electromagnetic spectrum on which the observations are made. We can observe a few parts of the spectrum from the Earth’s surface, while other parts are observable from either great heights or outside the Earth’s atmosphere. 

Specific information on the subfields of observational astronomy is given below.

Following are the types of observational astronomy:

• Observational astronomy

• X-ray astronomy

• Radio astronomy

• Infrared astronomy

• Optical astronomy

One of the historical methods of astronomy is optical astronomy; let’s understand it in detail:

Historically, optical astronomy is also known as visible light astronomy. We call it one of the oldest forms of astronomy. Images of observations were initially drawn by hand; however, in the late 19th century and most of the 20th century, images were prepared using photographic equipment. 

At present, the images are made by using digital detectors, particularly charge-coupled devices or CCDs, and then recorded on modern mediums. Though visible light extends from approximately 400 nm to 700 nm, we can use the same equipment to observe some near-ultraviolet and near-infrared emissions.

Opening the discussion with the lines that consider cyclic processes which constitute a very strong and powerful tool in final deductions based on the Second Law. The consideration of two points in configuration space that are infinitesimally close to one another as is represented by 1 and 2 in a particular process of quasistatic that takes a given system from state 1 to state 2. We can say that the heat exchange between the system and surroundings can be given as đrQ1→2 in it.

 

We ask whether it matters if this quantity is positive or negative. Select a second path that is irreversible that affects the same 1 → 2 change and that literally involves a heat exchange điQ1→2. This path latter is dashed on the diagram which is shown above being a process which is irreversible the path which lies outside the phase space appropriate to quasi-static processes. 

 

By the First Law which is given as đrQ1→2 = dE1→2 – đrW1→2, and điQ1→2 = dE1→2 – điW1→2.

 

Cyclic Process in Thermodynamics

 

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In this whole process of passing through a cycle that is working fluid, that is the system may convert heat from a warm source into useful work and even dispose of the remaining heat to a sink of cold. Which is thereby acting as a heat engine. The basic or major conversely that the cycle may be reversed and use work to move heat from a source which is cold and transfer it to a warm sink thereby acting as a heat pump. 

 

At each and every single point in the cycle, we can assume that the system is in thermodynamic equilibrium. So here we can conclude that the cycle is reversible, that is its entropy change is zero as entropy is a state function.

 

During a cycle that is closed, the system returns to its original thermodynamic state of pressure and temperature. The quantities or we can say the path quantities such as work and heat are process-dependent. For a full and proper cycle for which the system returns to its initial state, the first law of thermodynamics applies the following: 

 

The above clearly states that there is no energy change in the system over the cycle. We denote it as E_in which might be the heat and work that input during the cycle and E_out would be the work and heat output during the cycle. The first law which is of thermodynamics also dictates that the net heat input is equal to the network that is output over a cycle. We can account for heat denoted as Q_in as positive and Q_out as negative. 

 

What is the Cyclic Process?

Two classes that are of the primary nature of thermodynamic cycles are very powerful cycles and heat can pump the cycles. The cycles of power are cycles that convert some amount of heat input into a work mechanical output, while the pump of heat cycles transfers heat from low to high temperatures by using work that is mechanical as the input. 

 

Work Done in Cyclic Process

 

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The power of thermodynamic cycles is said to be the basis for the operation of heat engines which can truly supply most of the world’s power of electricity and run the vast majority of motor vehicles. The cycle of Power can be organized into two categories: that are the ideal and the real cycles. The encountered cycles which are in real-world devices that are the real cycles are difficult to analyze because of the presence of effect which is complicating friction. And, the absence of sufficient time which is given basically for the establishment of conditions of equilibrium. 

 

For the analysis purpose and design, and at times the model which is idealized ideal cycles are created. Here we can say that the power cycles can also be divided directly according to the type of heat engine they seek to model. The most common cycles which are used to model combustion which are internal engines are the cycle Otto which generally models gasoline engines. 

 

And, the cycle which is of the diesel which has the models diesel engines. The cycles that model combustion engines include the Brayton cycle, which models tribunals of gas, the cycle of Rankine which when models steam turbines the cycle which is Stirling which models hot air engines, and at times the Ericsson cycle which also models hot air engines.

Georg Simon Ohm, a German physicist, in the year 1827 deduced Ohm’s law which states that the current through a conductor is directly proportional to the potential difference applied across its 2 end-points. Mathematically, Ohm’s law is,

I ~ V

Where,

I = current b/w the 2 ends of the conductor

V = Potential difference applied across the conductor

Therefore,

I = V/R

Where R is the resistance offered by the resistor. Also written as,

V/I = R

The S.I. unit for Potential difference is Volts (V).

The S.I. unit for Current is Ampere (A).

The S.I. unit for resistance is Ohm, named after the scientist Georg Ohm who discovered it.

Ohm’s Law Explanation

A circuit is formed when a path is made for the charge to move through the conductor. This movement is caused due to the potential difference applied across the two end-points of the conductor. Current flows in the direction opposite to that of the flow of charge.

Potential difference refers to the amount of energy available for the current to move across the conductor. The potential difference across the two endpoints of the conductor is essential for the current to flow through the conductor. When current passes through the conductor, it gets some amount of friction or opposition from the conductor. This opposing force is called resistance. Resistance is very important, and many electrical devices operate based upon this concept of resistance and resistors—for example – electric heaters, steam iron, etc.

What is Ohm’s Law formula?

The formula for Ohm’s Law is,

V/I = R

Where,

V = Potential difference applied across the 2 endpoints of the conductor

I = Current flowing between the 2 endpoints of the conductor  

R = Resistance offered by the resistor

The resistance offered by the conductor depends upon certain factors. At a given temperature,

R ~ length of the wire

R ~ 1/cross sectional area

Mathematically,

R = pl/A

Where,

R = Resistance offered

p = Specific resistance or resistivity

l  = Length of the wire

A = Cross-sectional area

Sometimes more than one resistor is applied in a circuit. This can be applied both in parallel or series arrangement.

Series Arrangement 

Resistors are said to be placed in series if they are placed sequentially. Current flows through each of them one by one and current remains the same throughout the circuit. The total resistance of the circuit is obtained by adding the resistances.

R =  R1 + R2 + ….. + Rn

Parallel Arrangement

Resistors are said to be placed in parallel if the circuit is branched into separate paths in between. One end of all the resistors is attached to the point from which the circuit branches out and the other end of all the resistors is attached to the point, at which all the branched paths meet again, in the circuit. The flow of current through each resistor is different and has to be calculated individually.

I = I1 + I2

R=( 1/R1 + 1/R2 + …..+ 1/Rn)

What Factors Affect Resistance?

Electric current is caused due to the free flow of electrons in a system. Every system or conductor offers some resistance to this flow of current. The resistance offered by a conductor is dependent on a variety of factors like the type of its material, length, cross-sectional area, and temperature of the conductor. Let us discuss each of these in detail.

Material of the Conductor

Some elements have more conductivity as compared to others. Elements that allow free flow of current through them are called electrical conductors. Metals are good conductors. For example – iron. Certain elements that do not allow this free flow are called insulators.

Length of the Wire

The length of the wire is directly proportional to the resistance offered by the wire. It is because the current has to travel all through the conductor, which will increase the resistance offered to its flow.

Cross-sectional Area of the Wire

The thickness of the wire used as a resistor also plays an important role. The thicker the wire, the more current can pass through it easily. The resistance offered is indirectly proportional to the cross-sectional area of the wire. A wire of thinner diameter will offer more resistance.

Temperature of the Conductor

When conductors are heated they offer more resistance because the kinetic energy increases which inhibits the smooth flow of current. The temperature of a conductor is thus directly proportional to the resistance offered.

Uses of Ohm’s Law

Ohm’s law is commonly used in most of the electronic devices around us like amplifiers, mobiles, laptops, electric heaters, and also in rockets and spaceships. Some more applications of Ohm’s law are as follows.

• One of the most common examples of Ohm’s law in everyday life is the ceiling fan. The regulator of the fan, which regulates the speed of the fan uses Ohm’s law. The resistance is increased or decreased in the circuit by adjusting the regulator.

• Fuse designs in our households show the application of Ohm’s law.

• To calculate the power to be supplied to electric devices.

• To calculate the resistance of any circuit.