The Science Week

Coulomb's Law

noreply@blogger.com (Ishaan) — Tue, 18 Oct 2016 16:14:00 +0000

Coulomb's Law describes the force acting between static electrically charged particles. It helped in the development in the theory of electromagnetism.

Like charges repel and unlike charges attract. In this charged particles exert electric forces. Coulomb's law tells us about the electric force between two point

charges. Point charges are charges whose dimensions are very small, i.e., they can be considered single dimensioned.

Consider two charges q1 and q2 separated by a distance r. We are not going to talk about the magnitude or nature of the charges here.

Coulomb's Law states that the force between two point charges is:

Inversely proportional to the square of the distance between the charges

∴The force between two point charges increases as the force between them decreases and decreases as the distance between them increases.

2. Directly proportional to the product of magnitude of the charges.

∴The force between two point charges increases as the magnitude of the charges increases. It doesn't talk about the nature of charges and only tells us about the magnitude of force.

3. It acts along the line which joins the two charges.

Combining 1. and 2. :

When we remove the proportionality sign, a constant k is added.

This is the scalar form of the law, i.e, it only talks about the magnitude of force and not the direction. The direction is always along the line joining the two point charges and hence we add a unit vector. (I've not shown it here)

This is Coulomb's Law.

Constant k

k = 9.0 x 10⁹ N. m² / C²

The value of k was later experimentally determined and defined as :

Where ε₀ (epsilon knot) is the permittivity of free space = 8.85 × 10⁻¹² C²⋅N⁻¹⋅m⁻²

Bibliography:

https://en.wikipedia.org/wiki/Coulomb%27s_law

https://en.wikipedia.org/wiki/Vacuum_permittivity

Defects Of Vision- Simplified Notes

noreply@blogger.com (Ishaan) — Sat, 08 Oct 2016 15:55:00 +0000

The ciliary muscles control the curvature of the eye lens and hence alters the focal length of the eye lens. For clear vision the image of the object must be formed on the retina. Sometimes the image of the object might not be formed on the eye's retina, causing difficulty in seeing the object clearly. This can happen due to factors such as change in the curvature of the eye and damage to the eye lens.

There are mainly 4 defects of vision :

Near-sightedness (Myopia)
Far-sightedness (Hypermetropia)
Presbyopia
Astigmatism

Nearsightedness

It is also called myopia.
A person suffering from this defect cannot see distant objects clearly.
This is because the light rays from distant objects converge before the retina even when the focal length of the eye is maximum.
Further strain does not help.

Causes:

Eye lens is too thick
Radius of eye is larger than usual. i.e more than 2cm.
Decrease in the maximum focal length which is caused when the cillary muscles holding the eye lens cannot relax completely and have some tension.

Treatment:

The treatment is simple and painless.
Since the light rays are converging too much, they are made to diverge a bit before they enter the eye. This is done by using a diverging lens or a concave lens.
IMPORTANT: The convex lens makes it appear that the light rays from distant objects are coming from the apparent far point of the eye.

Farsightedness

A person suffering from this defect can see distinct objects clearly but is unable to see clearly the object close to his eyes.
In this the rays coming from close objects focus behind the retina. Therefore the diverging power of the lens is reduced.
In this the least distance for clear vision increases and hence the person is unable to see objects placed between the apparent near point and the normal fear point (25cm).
This usually occurs to elder people. This defect makes it hard to read textbooks ad newspapers.

Causes:

It is also known as hypermetropia.
It occurs when the eye lens is thinner at the center.
Decrease in the radius of eyeball.
Increase in the minimum focal length of the eye lens and hence the person is unable to decrease the focal length to view close by objects. The cillary muscles even in their most strained state are unable to decrease the focal length.
Weakening of the cillary muscles. This condition in which hypermetropia is caused due to weakening of the cillary muscles is known as presbyopia.

Treatment:

The treatment is simple and painless. Since the rays are diverging too much, they are made to converge a little before they enter the eye. This can be done by using a converging lens or a convex lens.
The convex lens makes it appear that the light rays from the close objects are coming from the apparent near point of the eye.

Presbyopia

A person suffering from this eye defect is unable to see close objects clearly. This is similar to hypermetropia and is cause due to weakening of the cillary muscles as mentioned above.
The near point of the eye increases.

Causes:

This is mainly seen in older people and is caused to weakening of the cillary muscles.
The flexibility of the lens decreases.

Treatment:

The treatment is simple and painless. Since we cannot see close objects clearly, a convex lens is used.

Astigmatism

A person suffering from this defect is unable to see all the directions clearly. In this the person is unable to focus on horizontal and vertical planes at the same time.

Causes:

It is caused when the eye develops different curvatures along different planes. Hence there is a change in the shape of the eyeball.

Treatment:

The treatment is simple and painless. Lenses with different curvatures along different planes are used. This compensates for the deshaping of the eyeball. These lenses are called cylindrical lenses.

RMS Value Of AC (Alternating Current)

noreply@blogger.com (Ishaan) — Fri, 19 Aug 2016 19:06:00 +0000

For understanding what RMS (root square value) of AC current is you will have to first understand what AC current is. AC current is basically the type of current in which the charges flowing through a conductor periodically reverse their directio
n.

So instead of flowing in one direction the electrons vibrate about their mean position. The vibration of the electron is similar to that of the movement of a pendulum. The current is maximum when the electron is at the center and is zero when the electron is at the extreme position.

RMS Value Of AC

In AC the magnitude of electricity changes continuously and the direction changes periodically.

Alternating current has a maximum value and a minimum value (only their signs differ). The maximum current is called the peak value of current and is denoted by I_o. (read as I knot).

Let’s consider a bulb. We connect this bulb to an AC supply. Let the maximum current (Io) flowing through this circuit be 10A. Does this mean that a steady 10A current is flowing though the bulb? No, the magnitude of current keeps changing. At one instant it can be 1A and at another it can be 8A. So if someone asks you how much current is flowing though this bulb, then what will your answer be? If your thinking 10A then your wrong because it is not a steady flow and the current keeps changing. Lets find the answer to this question.
AC shows all the effects that DC shows. These effects include heating effect (I²RT), magnetic effect etc. For all these effect we have a formula to calculate the magnitude of the effect in which one of the factor is current. So for calculating the magnitude of heat produced by AC, which value of AC will you put? The maximum value or the minimum value? The answer is none of these. We use the average current flowing through the appliance and this average current is known as RMS value AC.

Consider the following graph. The x-axis represents time and the y-axis represents the EMF. Since we are using AC current the EMF changes at every given moment.
---------

Work done by this current = Power x time = I²RT

At time T₁, the current is less and so the work done is less. At time T2, the current is more and hence the work done is more.

Now, we calculate the average work done. When we calculate the average current, we notice that in I²RT, the RT part is common. Only the current changes. Hence we actually calculate the average of I²

∴ I_avg² = I₁²+ I₂² + I₃² . . . . I_n² / n
∴ I_avg = √I₁²+ I₂² + I₃² . . . . I_n² /n (under root of I_avg² )

I_avg is know as root mean square, that is, mean of root of squares.

We took the squares of current in the beginning as in the work formula, it is I² and not I.

→ I_{avg =}I_RNS

Consider the following example.

We want to heat a bucket of water upto a certain temperature in 1 hour. For this purpose we use DC and AC separately.

→ CASE 1 : 10A AC

The AC used is given by the following graph.

---------

Since the current is not constant in an AC supply, the heating will also be different. That is, sometimes it will heat the bucket using 10A current and sometimes 0A current. We observe that the bucket is heated up to the specific temperature in 1 hour.

→ CASE 2 : 10A DC

Since in DC, there is constant current, the bucket is heated by the same amount of power. We observe that it took the bucket 45 minutes to heat up to the specific temperature.

∴ We conclude that 10A DC is doing more work as compared to 10A AC.

→ CASE 3 : 8A DC

The current supply has decreased from 10A to 8A DC. We observe that it took 50 minutes to heat the bucket to the specific temperature.

∴ We conclude that 8A DC is doing more work as compared to 10A AC.

→ CASE 4 : 6A DC

The current is now reduced to 6A. We observe that it took 1 hour 10 minutes to heat the bucket.

∴ We conclude that 10A AC is doing more work as compared to 6A DC.

By doing this several times, i.e. by trial and error, we find that 7A DC heats the bucket in 1 hour. Hence we can say that 7A DC is doing the same amount of work as compared to 10A DC.

So if someone asks us the magnitude of AC we used to heat the bucket we won’t tell them 0-10A or anything like that. We tell them that we used 7A AC to heat the bucket. This is because the 0-10A AC did the same amount of work the 7A DC did

∴ 0-10A AC = 7A DC

This comparison is done on the basis of the work done.

∴ 7A is called the RMS (root mean square) value of AC because we used work to derive it and average work is the average of electric current.

∴For calculating any effect of AC current like magnetic effect and heating effect, we put the RMS value (7A in this case) in the formulas.

NOTE: If you go to the electrical store and buy an electric heater and someone asks you how much electric current this heater uses, then you will tell the RMS value of the devise (which is usually specified).

Now,

V=IR (Ohm's Law)

∴V_RNS= I_RNS X R

In India the domestic voltage is 220V. This is the RMS voltage.

The derivation of the formula to calculate the RMS AC includes integration. For now I'm only giving you the direct formulas and not the integration part, however comment down below if you want me to show the derivation.

Where I= peak value of current of AC current.

Where V= peak value of voltage in AC.

Mass Defect and Nuclear Binding Energy - Simplified Notes

noreply@blogger.com (Ishaan) — Wed, 03 Aug 2016 19:54:00 +0000

Nuclear Binding Energy

Nuclear binding energy is the energy required to break the nucleus into its constituent particles. (OR) It is the energy released when protons and neutrons come together to form a nucleus.

Lets say we have He-4 atom. This has 2 protons and two neutrons in its nucleus. These protons and neutrons are present as one mass in the nucleus and are stuck together something called nuclear strong force (we will talk about this later).

So, the nuclear binding energy is the amount of energy required to separate these protons ans neutrons so that they aren't together.

Now suppose we have 2 protons ans 2 neutrons . We want to form a nucleus by combining these particles. To combine them, they are brought close to each other. (we will talk about the formation of a nucleus under nuclear strong force). When these particles combine, they release a certain amount of energy. This energy released is known as nuclear binding energy.

Mass Defect

Mass defect is the difference of mass of the the composite particles and the overall mass of the atom.

This means that when we predict the mass of an atom by adding the mass of the constituent particles (protons and neutrons), we find that the mass is less than the actual mass when we weigh the atom.

It will become clearer after the following example:

Calculate the mass of a He-4 atom.

we know that He-4 atom consists of 2 protons and 2 neutrons.

mass of 1 proton= 1.00727647 u. (atomic mass units)

mass of 1 neutron= 1.008664 u.

(these absolute masses were obtained by weighing the particles)

∴ total mass= 2.(1.00727647) + 2.(1.008664)

= 2.01455294 + 2.017328

= 4.03188094 u.

This is what we predicted the mass would be of a He-4 atom. Lets call this the predicted mass.

When scientists weighed 1 atom a He-4 atom they found that its mass was 4.002602 u! Lets call this the actual mass.

We notice that there is a difference between the predicted mass and the actual mass of an He-4 atom. This difference between the predicted mass and the actual mass is known as the mass defect.

∴ predicted mass - actual mass = mass defect

∴ 4.03188094 u - 4.002602 u = mass defect

∴ 0.02927894 u = mass defect.

Hence we can say that the mass of reactants > mass of product formed.

How is this possible?

This difference in mass is because when the particles combine, a part of the reactants mass gets converted into energy. This energy is the nuclear binding energy.

∴ Nuclear binding energy and mass defect are kind of the same things.

We said that part of the reactants mass got converted into energy. Einstein gave the famous equation E=mc^2

where E is the energy equivalence of the mass

m= mass of substance

c = speed of light in vacuum (3 x 10^8 m/s)

Back to our problem, we had 0.02927894 u of mass that had got converted into energy. Lets calculate how much this energy actually is by using Einsteins equation.

1u = 1.6 × 10^ -27 Kg

∴ 0.02927894 u = 1.66054 × 10^-27 ×0.02927894 Kg
= 0.046846304 × 10^-27 Kg
= 4.6846304 × 10^-29 Kg

Now put this value in E=mc^2:

∴ E= (4.6846304 × 10^ -29) × (3 × 10^8)^2
= 4.6846304 × 10^-29 × 9 × 10^16
= 4.21616736 × 10^-13 J

This is the amount of energy released when a He-4 nucleus is formed (or) It is the amount of energy required to break a He-4 nucleus into its constituent particles (2 protons and two neutrons). This energy is called Nuclear Binding
Energy.

Quantum Numbers - Simplified Notes

noreply@blogger.com (Ishaan) — Sat, 23 Jul 2016 20:08:00 +0000

Quantum numbers are like the address of an electron. It tells where an electron is located around the nucleus of the atom. Just just we have home addresses, even electrons have an address of their location. Some parts of our address are not so specific of our location whereas other parts are. So, quantum numbers are like lines of your home address.There are 4 quantum numbers.

Principal Quantum Number (n)

This is like the city name. It is not very specific about the location of the electron.

This number describes the energy level/orbit/shell in which the electron is located. (energy level is the same thing as orbit or shell)

Neil Bohr said that the atom has various energy levels around the nucleus. The principal quantum number tells us in which energy level the electron is located.

There can be many energy levels around the nucleus but normally we only deal with the first 4 or 5.

∴ n=1, 2, 3, 4.....
There are names given to the shells.

n=0 → k shell
n=1 → l shell
n=2 → m shell
n=3 → n shell

Azimuthal or Subsidary Quantum Number (l)

This quantum number is like the name of the street in our address. It is more specific as compared to the principal quantum number.

This Quantum number describes the subshells which are present within a shell. Moreover, it also describes the shape of the orbitals about which we will talk about later.

There are a specific number of subshells present within each shell. Hence the number of subshells in a shell is related to shell number which is described by the principal quantum number as follows:

l= 0→ n-1 (read as l is equal to all values from zero to n minus one)

So for a given quantum number n, l can be any value from 0→n-1

Example: Principal quantum number 3

∴ l=0→n-1

∴ l=0→3-1

∴ l=0→2

∴ l can take up value 0, 1, 2

Example: Principal quantum number 4

∴ l=0→n-1

∴ l=0→4-1

∴ l=0→3

∴ l can take up value 0, 1, 2, 3

Here 0 is counted as a subshell and hence it means something.

l=0 → s-subshell l=2 → d-subshell

l=1 → p-subshell l=3 → f-subshell

∴The 3rd shell has 3 subshells- s, p, d

and the 4th shell has 4 subshells s, p, d, f

We also observer that if we move up by one shell we add subshell just like in the above examples.

Magnetic Quantum Number (m)

First come the shells. Within the shells are located the subshells and withing the subshells are located orbitals! The magnetic quantum number represented by 'm' tells us which orbital the electron is located in. This like the house number of the electron.

This quantum number tells us the orientation.

NOTE: EACH ORBITAL CAN ACCOMMODATE A MAXIMUM OF 2 ELECTRONS.

Since orbitals are within subshells, there is a mathematical representation between the subshells and orbitals. This is given by:

m= -l→ +l (m equals all values from -ive l to +ive l)

This includes 0.

Example: For p subshell

since we are given p subshell, l=1

∴ m= -1 → +l

∴ m= -1, 0, 1

∴ there are 3 orbitals within subshell p.

∴ since each orbital can accommodate a maximum of 2 electrons and p subshell has 3 orbitals, we conclude that p subshell can accommodate a maximum of 6 electrons.

Example: How many electrons can there in s-subshell?

For s-subshell, l=0.

∴ m= -0 → +0

∴ m= 0

There is only one orbital within s-subshell.
(0 doesn't mean that there are zero orbitals. 0 is considered as 1 orbital!)

∴ since each orbital can accommodate a maximum of 2 electrons and s-subshell has 1 orbital, we conclude that s-subshell can accommodate a maximum of 2 electrons.

If you observe carefully you will notice a relation between the shell and the number of orbitals present in it. This is:

number of orbitals present in a shell=n2
where n is the shell number, i,e, k, l , m, n, etc.

Here another important relation:

The maximum number of electrons that can occupy a specific energy level is 2n2

where n is the shell number. This is just a continuation of the previous relation if you think about how that 2 appeared there.

Spin Quantum Number (s)

This is the simplest kind of quantum number. It basically tells us in which direction the electron is spinning. There can be only 2 values of the spin quantum number, i,e, -1/2 and +1/2. And the awesome part is that there is no mathematical relation to find the spin quantum number. We cant exactly determine the direction of its spin.

-1/2 means that the electron is spinning downwards.

+1/2 means that the electron is spinning upwards.

∴ s= 1/2 or +1/2.

In subjective tests, for this quantum number its better to mention both 1/2 and +1/2 because we cannot calculate the direction of spin. In objective tests if you get the other 3 quantum numbers it really doesn't matter weather the option says 1/2 or +1/2.

Now we draw to the end of this chapter. But we are missing one thing. How do we compile the address of the electron and write it in an easily understandable way? Here's how:

Example: If the electron is present in n=3 and l=2.

∴ we know that n=3 and l=2
∴ we write this as 3d
were 3 is the shell number (n) and d is the subshell number (l).

We can calculate the number of orbitals present in l subshell by using the relation m= -l→ +l. In this case we get 5 possibilities of m, i,e, -2, -1, 0, +1, +2.
Since the electron can be in any of these orbitals we don't represent them.

We also know that the maximum electrons present in the d-subshell is 6. So a completely filled 3d is represented by 3d6.

Wave Front Simplified Explanation

noreply@blogger.com (Ishaan) — Sun, 10 Jul 2016 18:48:00 +0000

Wave Front

Definition: It is the locus of points in the same phase.

Let us take a beam of light. A beam of light doesn't consist of one wave of light but many as shown in the image.

In the second image, I have drawn points on the waves that are in the same phase(the crests). When we connect these dots, we get a straight line. This is the wave front of these waves.

There are 3 types of wave front:

Spherical wave front
Plane wave front
Cylindrical wave front

Spherical Wave Front

Here, the shape of the wave front is a sphere, just like a football.
A spherical wave front is created when the source of waves is a point source, i,e, dimensionless.

For example, when we throw a stone in a lake, ripples are formed in all directions surrounding the point of impact. If we look from the top, it will look like concentric circles. If we join the points in the same phase, we obtain a circle. But this is only from the top. If we keep doing this from all the angles, we obtain a sphere. This is the spherical wave front.

Just try to picturize a 3D image in your mind.

A point.
Waves coming out of this point from all 3 axis's.
Points in the same phase are represented as dots in all the waves.
Connect these dots. You get a sphere!

Plane Wave Front

A plane wave front is obtained when the source of waves is located at infinity.

When we says that the source of waves is at infinity, we mean that the waves of light are so almost parallel, that they are assumed parallel(actually they are diverging waves).

A plane wave front looks like a sheet of paper. When we observe it from the front, it looks like a plane, whereas if we view it sideways, we see parallel lines.

Cylindrical Wave Front

A cylindrical wave front is obtained when the source of waves is a line source, i,e, it is like a lightsaber.

A cylindrical wave front looks like a cylinder.

If we draw the wave front for one plane, we will obtain a concentric circle. But is we continue to draw the wave front of different planes,we will obtain more concentric circles which combine to form a cylinder.

Wave Phase - Simplified Explantion

noreply@blogger.com (Ishaan) — Sat, 09 Jul 2016 19:28:00 +0000

WAVE PHASE

This is used to describe a location within a specific wave.

Consider the following wave. For one wavelength, say from A to E, all the points are doing different things i,e, they all are moving in different directions and don't represent the same place... obviously. Basically, all these points are different and represent different things. So, we say that all the points from A to E are not in phase.

Now, lets consider two cycles of the wave. From A to I. By cycles I mean wavelengths. Here, we use wave phase to talk about all the points that are kind of the same. You will understand better by an example.

Look at points A and E. Both of them are doing the same thing, i,e, they are moving upwards. Now the most important both of the points represent the same location for one wave cycle. So, A represents the beginning of wave cycle AE just as E represents the beginning of wave cycle EI.

Similarly, B, F, J, N are in phase.

Similarly, C, G, K, O are in phase.

Similarly, D, H, L are in phase.

Hence we can say A and E are kind of the same thing. Hence, we use wave phase to talk about all the points in multiple cycles of the wave that are located at the same place within 1 cycle.

Lets talk about points A and C. Both of them are located at the same level but they are doing the same thing. A is moving upwards whereas C is moving downwards. So points A and C are out of phase.

Using Wave Phase To Define Wavelength

Wavelength is distance between two consecutive points which are in the same phase.

So now you don't have to define wavelength as the distance between two consecutive crests or troughs (even though its right). Defining wavelength in terms of phase sounds more precise.

Just remember, any two consecutive crests are always in the same phase as are two consecutive troughs.

Everything You Need To Know About Nuclear Fission simplified

noreply@blogger.com (Ishaan) — Thu, 30 Jun 2016 19:01:00 +0000

Nuclear Fission

Fission just like binary fission in Biology means splitting.

It is the process in which a heavy atom splits into two or more lighter atoms that are more stable than the heavy atom. Here by the term heavy nucleus I mean an atom that has a pretty large mass number, say 92 (Uranium).

Just remember, anything that can undergo fission or split is called fissile.

Splitting of heavy atoms provides us with a large amount of energy which is used in nuclear power plants to generate electricity, in nuclear submarines or even bombs!

Let's consider the example of Uranium 235.

Uranium 235 is quite unstable. What we do is, we bombard the nucleus of U235 with a neutron. Understand bombarding like smacking. When we do this, the neutron becomes part of the nucleus of the U235 atom and hence increases its mass number by 1. (mass no. = no of protons + neutrons).

∴ U236 is formed. Observe that there is no change in its atomic number and hence we have created an isotope of Uranium.

This U236 is highly unstable. Much more unstable than U235. It is infact so unstable that it immediately wants to become lighter and hence immediately splits into two new atoms creating Krypton(Kr) and Barium(Ba) and 3 little neutrons.

Something very important happens now. The 3 little neutrons go and collide into another U235 atom each converts itself into U236 which splits into 3 new neutrons along with Kr and Ba. Hence creating 9 new neutrons. These 9 neutrons repeat the same process. This is called a chain reaction.

Projectile: It is the particle which is used to bombard the nucleus of atoms for causing the atom to split is called a projectile. In the example of U235, a neutron was the projectile.

Chain Reaction: It is a process in which the particle used to start the reaction gets produced over and over and is responsible for the carrying forward of the reaction.

Every time U236 splits, it releases a little amount of energy. But when so many atoms of U236 split because of the chain reaction, the net energy is a lot.

In the fissioning of uranium some mass of uranium disappears(is lost). This mass gets converted into energy. Einstein gave the equation E=mc ²

where E= energy

m= mass

c= speed of light in vacuum (3×10⁸ m/s)

∴ There is conservation of mass and charge in nuclear fission.

Uranium is the only element that is capable of undergoing nuclear fission. Most of the heavy elements (90-100) are capable of this.

Plutonium was the fissile element used in the bomb dropped in Nagasaki in 1945.

Even though a small amount of mass gets converted into energy notice that the speed of light is squared. So even a small amount of mass is capable of producing a huge amount of energy.

Elements that occur in nature are quite stable, so the probability of them undergoing nuclear fission on their own is pretty small. So nuclear fission is carried out by bombarding the heavy nucleus with a slow moving particle such as a neutron.

Another way to understand how nuclear fission works is by the Liquid Drop Model.

Liquid Drop Model

It states that fission works in the same way as the splitting of a drop of water when another drop of water is added to it. Take a drop of water. From the top, drop another drop of water over it. You will notice that the drop elongates and splits into two water droplets smaller in size.

In nuclear fission, the original drop of water is the heavy unstable atom and the second drop of water is the projectile. When the projectile bombards the heavy water drop, it becomes unstable first, then elongates and finally splits into two smaller water droplets.

Mutual Inductance and Transformers simplified

noreply@blogger.com (Ishaan) — Tue, 28 Jun 2016 16:36:00 +0000

Mutual Induction (M)

It is the phenomenon in which change of current in a coil causes an EMF to be induced in another coil. The current in which we supply current is called primary coil and the coil in which an EMF is induced is called the secondary coil.

Mutual induction was one of Faraday's discoveries.

Lets consider the following example.

Connect a coil to an AC source. This coil is the primary coil. Because we are passing electricity through it, it will generate a magnetic field, represented by the dotted lines. Since we have used AC current, the current keeps alternating and hence the magnetic field keeps changing.

Now introduce a second coil in the magnetic field of the primary coil. According to Lenz's law the new coil will try and oppose the magnetic flux of the primary coil and hence an EMF is induced in it. This is the secondary coil.

This is the basic concept of mutual induction in which change of current in one coil induces an EMF in the second.

The concept of mutual induction is the principal of generates and transformers.

Transformer

A transformer is an electrical devise that is used to convert AC current at one voltage and deliver it at another. It delivers the same frequency of current. There is a little loss in power in transformers.

The principal of transformers is mutual inductance or some might say electromagnetic induction.

A transformer can increase the voltage and decrease the current (step-up) or it can reduce the voltage and increase the current (step-down). A transformer might look pretty intimidating but its not. It doesn't even use any moving parts!

A transformer can transform voltage with alternating current but not with direct current. This is because if we supply direct current there will be no change in magnetic flux and hence not current will be induced in the secondary coil.

The primary and the secondary coil are wrapped around a frame. The same magnetic flux flows through the two coils.

Vs - net voltage in secondary coil

vs - voltage in each secondary coil

Ns - number of loops in secondary coil

Vp - applied voltage in primary coil

vp - voltage in each primary coil

Np - number of turns in primary coil

Since the loops of the secondary coil are connected in series the net voltage across its ends is equal to voltage per turn multiplied by the number of turns.

∴ Vs= vs × Ns ------ 1

Since the same magnetic flux is passing through the primary and secondary coil, the voltage per turn is the same.

∴vp = vs --------2

The voltage per unit turn in the primary coil depends upon the number of turns and the applied voltage. The three are related as follows.

∴ vp= Vp/Np ------3

from 2 and 3 we get,

vs = Vp/Np ------ 4

Put this into 1

∴ Vs = Vp/Np × Ns

From this we draw a crucial conclusion. If the secondary coil has more turns as compared to the primary coil, then the voltage is increased and hence the transformer acts as a step-up transform.

If the secondary coil has fewer turns as compared to the primary coil, then the voltage is lowered and hence the transform is a step down transformer.

Since energy is always conserved, Vs × Is = Vp × Ip

The core of transformers are laminated. This means that is not a single block of metal, but its thickness is built by combining numerous thin sheets of aluminium or iron. The core of the transformer is not meant to conduct current. But since there is a magnetic flux in it, there will be an induced current. This current is known as eddy currents. These eddy currents heat up the system and hence waste a lot of energy. The core is thus laminated to reduce the effects of these eddy currents.

There are many ways by which heat is waster while transferring power from the primary to the secondary coil. These include: eddy current, hysteresis loss and I2R loss.

This energy is dissipated as heat. To cool the system, the transformer is immersed in cooling oil. The oil dissipates the current by convection currents which exits through the radiator fins.

Moreover, the oil expands due to this heating. To make space for this increasing volume, a tank is attached to the top of the transformer.

Electron Cloud Model simplified

noreply@blogger.com (Ishaan) — Mon, 27 Jun 2016 19:20:00 +0000

In this depiction we see a spinning fan. Can you see the blades? Can you tell their location at a given time? Not clearly right? The electron cloud model works in a similar way. The blades being the electrons.

Bohr talked about the electrons orbiting the atom's nucleus in a similar way planets orbiting the sun. Bohr's model is useful to understand the properties of the elements and their chemical interactions. However, it doesn't explain a lot of theories including the Stark effect, Zeeman effect and the behaviour of electrons except for the simplest types of atoms such as Hydrogen.

The Electron Cloud

The electron cloud model also known as quantum mechanical model was developed in 1925 by Erwin SchrÖdinger and Werner Heisenberg. This is one of the newer models of the atom. He used mathematics to claim that it is impossible to know for certain where an electron is at any given time. This is similar to the Heisenberg uncertainty principal.

How Does It Look Like?

It consists of a positively charges nucleus surrounded by a spherical space.

This is how the electron cloud model of the helium atom looks like. At the centre are two protons and two neutrons. Surrounding the nucleus is an electron cloud which cover the nucleus in all 3 dimensions.

You might notice that the coloured differently. It is darkest near to the nucleus and gets lighter as we travel away. This colour gradient is based on electron probability: The likelihood of finding an electron in a certain location. Hence we can say that is is more likely to find an electron close to the nucleus and the probability of its location decreases as we more further away.

Electron movement around the nucleus takes on the appearance of a cloud, and wherever the cloud is densest is where there is the highest probability of finding an electron.

Difference b/w Bohr and Schrodinger's Models

Bohr: He assumed that the electron is also a particle.

SchrÖdinger: He assumed that the electron is a wave.

Bohr: He said that the nucleus was orbited by electrons.

SchrÖdinger: He said that the nucleus was surrounded by a cloud of electrons.

Basically Bohr said that the electrons orbited the nucleus in specified shell/orbit/energy level whereas SchrÖdinger said that the location of electrons was all based on probability.

Self Inductance Simplified Explanation

noreply@blogger.com (Ishaan) — Sun, 26 Jun 2016 10:31:00 +0000

Self Inductance :

It is defined as the induction of a voltage in a current carrying wire when the current in the wire is itself changed. Hence changing current in a circuit generates a new voltage in the circuit. Hence it is called self inductance.
[or]
It is the property of a coil/conductor by which it opposes change in current in itself.

We know that B ∝ I and Φ ∝ B

∴ Φ ∝ I

∴ Φ= LI
(where L is the coefficient of self induction)

If current in the coil changes at a rate ΔI = dI/dt, then EMF induced in coil due to change in its own current is: e= dΦ/dt

(where e is induced EMF)

∴ e= L[dI /dt]
This is the magnitude. The induced EMF always opposes the very cause producing it.

∴ with direction it is written as

e= - L[dI /dt]

Here's the explanation:

We have taken two circuits. In the 1st one, we have a battery with EMF = E, a galvanometer, a resistance R, and of course connecting wires.

In the 2nd circuit, all the components remain the same as in the first circuit except that we have added a loop in the circuit.

When we complete the circuit in case 1, when we apply ohms law [ V=IR], the value of current is E/R. The reading of the galvanometer suddenly increases E/R. This is because there is not much resistance in the circuit.

Now lets talk about case 2. When we complete the circuit, current flows in the loop. Due to this the loop produces a magnetic field. In the time taken to reach E/R, the current in the circuit is increasing. The current in the loop produces a magnetic field. Now, while the current is increasing in the loop, the magnitude of the magnetic field also changes(it increases). Since the magnitude of magnetic field is changing, the magnetic flux associated with the loop is also changing in that small time interval from 0 current to E/R.

Hence, change in value of current creates a change in the magnitude of magneric field of the loop which causes a change in the magnetic flux associated with the loop.

To oppose the change in magnetic flux the loop generates its own EMF and hence induces a current which flows opposite to the original current.

In the above picture, the red arrows depict the direction of induces current in the loop. Because of this extra resistance of current, the current in the circuit rises slower compared to the first circuit. Hence the galvanometer takes more time to reach E/R. But this is only when the current in the circuit is rising, one it reaches E/R, there would no longer be a change in magnetic flux and hence the induced current disappears.

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3D With '3Doodler' Pen

noreply@blogger.com (Ishaan) — Sun, 26 Jun 2016 07:45:00 +0000

The 3Doodler is a 3D pen that allows you to create 3D arts. It was developed by Peter Dilworth, Maxwell Bogue and Daniel Cowen of WobbleWorks, Inc. For long, the concept of 3D printing was thought of science fiction but over the last few decades 3D printers have become wide spread and are used for all sorts of
purposes from making simple 3D models to making complex body organs. However, the many might find the 3D printer hard to use because of its complicated software and hardware. But now a company called 3Doodler has introduced this amazing pen which allows us to draw freehand sketches in mid air.

It makes use of plastic thread made of Acrylonitrile butadiene styrene [ABS] and poylactic acid [PLA]. It uses these plastics by heating them and forcing them out though a nozzle which cool down almost instantly forming a solid stable structure.

In many ways the 3Doodler works like a glue gun. A heating element heats the plastic and forces it out. The glue gun uses a hand pump which forces the glue out which makes it pretty messy to use. So the challenge for the team was to create a way to make the plastic flow out more steadily and smoothly. For this they used a motor which propels the plastic out smoothly.

The 3Doodler Create far exceeds the 127-degree F (53 degrees C) maximum temperature allowed for children's products, as set by the EU Toys Safety Directive. To solve this problem 3Doodler teamed up with material scientists and together developed a new types of plastic which was biodegradable and child friendly and which melts between 113 degrees and 122 degrees Fahrenheit (45 to 50 degrees C).