Joules law

We all know about the heating effect of electric current , when it flows through a circuit due to collision between electrons and atoms of wire. But precisely how much heat is generated during electric current flow through a wire, on what conditions and parameters does it depend?
To solve this problem, Joule invented a formula which explains this phenomenon accurately. This is known as Joule’s law. This law is explained in detail below.

Joule’s Law of Heating

• 

The heat which is produced due to the flow of electric current within an electric wire, is expressed in Joules. Now the mathematical representation or explanation of Joule’s law is given in the following manner.

i) The amount of heat produced in electric current conducting wire, is proportional to the square of the amount of electric current that is flowing through the circuit, when the electric resistance  of the wire and the time of electric current flow is constant.
i.e. H ∝ i2 (When R & t are constant)
ii) The amount of heat produced is proportional to the electric resistance of the wire when the electric current in the circuit and the time of electric current flow is constant.
i.e. H ∝ R (when i & t are constant)
iii) Heat generated due to the flow of electric current is proportional to the time of electric current flow, when the resistance and amount of electric current  flow is constant.
i.e. H ∝ t (when i & R are constant)
When these three conditions are merged, the resulting formula is like this -
  i.e. H ∝ i2 R t
Here ‘H’ is the heat generated in Joules, ‘i’ is the electric current flowing through the circuit in ampere and ‘t’ is in seconds. When any three of these are known the other one can be equated out.
Here, 'J' is a constant, known as Joule's mechanical equivalent of heat. Mechanical equivalent of heat may be defined as the number of work units which, when completely converted into heat, furnishes one unit of heat.
Obviously the value of J will depend on the choice of units for work and heat.
It has been found that
J = 4.2 joules/cal (1 joule = 107 ergs)
It should be noted that the above values are not very accurate but are good enough for general work.
Now according to Joule's law I2Rt = work done in joules electrically when I ampere of electric current are maintained through a resistor of R ohms for t second.
Therefore
H =i2 Rt joules/4.2joules/cal
   = i2Rt/4.2 cal 
By eliminating I and R in turn in the above expression with the help of ohm's law we get alternative forms as 
H=0.24 V I t cal = 0.24 v2 t/R cal
Video on joules law.

Newton's laws of motion

Let us begin our explanation of how Newton changed our understanding of the Universe by enumerating his Three Laws of Motion.

1-Newton's First Law of Motion:

 Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

This  recognize us the Galileo's concept of inertia, and so this is often known as the "Law of Inertia"

2-Newton's Second Law of Motion:

 The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.

3-Newton’s Third law of motion :

For every action there is an equal and opposite reaction.

This law is exemplified by what happens if we step off a boat onto the bank of a lake: as we move in the direction of the shore, the boat tends to move in the opposite direction (leaving us facedown in the water, if we aren't careful!).

Kirchoff's laws

Kirchhoff Current Law and Kirchhoff Voltage Law

There are some simple relationships between currents and voltages of different branches of an electrical circuit. These relationships are determined by some basic laws that are known as Kirchhoff laws or more specifically Kirchhoff Current and Voltage laws. These laws are very helpful in determining the equivalent electrical resistance or impedance (in case of AC) of a complex network and the currents flowing in the various branches of the network. These laws are first derived by Guatov Robert Kirchhoff and hence these laws are also referred as Kirchhoff Laws.

Kirchhoff's Current Law

In an electrical circuit, the electric current flows rationally as electrical quantity. As the flow of current is considered as flow of quantity, at any point in the circuit the total current enters, is exactly equal to the total electric current leaves the point. The point may be considered anywhere in the circuit.
Suppose the point is on the conductor through which the currentis flowing, then the same currentcrosses the point which can alternatively said that the electric current enters at the point and same will leave the point. As we said the point may be anywhere on the circuit, so it can also be a junction point in the circuit. So total quantity of electric current enters at the junction point must be exactly equal to total quantity of electric currentthat leaves the junction. This is the very basic thing about flowing ofelectric current and fortunately Kirchhoff Current law says the same. The law is also known as Kirchhoff First Law and this law stated that, at any junction point in the electrical circuit, the summation of all the branch currents is zero. If we consider all the currents enter in the junction are considered as positive current, then convention of all the branch currents leaving the junction are negative. Now if we add all these positive and negative signed currents, obviously we will get result of zero.
The mathematical form of Kirchhoff's Current Law is as follows,

We have a junction where n number of beaches meet together.

Let's I1, I2, I3, ...................... Im are theelectric current of branches 1, 2, 3, ......m and
Im + 1, Im + 2, Im + 3, ...................... In are the electric current of branches m + 1, m + 2, m + 3, ......n respectively.

The currents in branches 1, 2, 3 ....m are entering to the junction.
Whereas currents in branches m + 1, m + 2, m + 3 ....n are leaving from the junction.

So the currents in the branches 1, 2, 3 ....m may be considered as positive as per general convention and similarly the currents in the branches m + 1, m + 2, m + 3 ....n may be considered as negative.

Hence all the branch currents in respect of the said junction are -
+ I1, + I2, + I3,................+ Im, − Im + 1, − Im + 2, − Im + 3, .................. and − In.
Now, the summation of all currents at the junction is-
I1 + I2 + I3 + ................+ Im − Im + 1 − Im + 2 − Im + 3..................− In.
This is equal to zero according to Kirchhoff Current Law.

Therefore, I1 + I2 + I3 + ................+ Im− Im + 1 − Im + 2 − Im + 3..................− In = 0.
The mathematical form of Kirchhoff First Law is ∑ I = 0 at any junction of electrical network.

Kirchhoff's Voltage Law

This law deals with the voltage drops at various branches in an electrical circuit. Think about one point on a closed loop in an electrical circuit. If someone goes to any other point on the same loop, he or she will find that the potential at that second point may be different from first point. If he or she continues to go to some different point in the loop, he or she may find some different potential at that new location. If he or she goes on further along that closed loop, ultimately he or she reaches the initial point from where the journey was started. That means, he or she comes back to the same potential point after crossing through different voltage levels. It can be alternatively said that net voltage gain and net voltage drops along a closed loop are equal. That is what Kirchhoff Voltage lawstates. This law is alternatively known as Kirchhoff Second Law.

If we consider a closed loop conventionally, if we consider all the voltage gains along the loop are positive then all the voltage drops along the loop should be considered as negative. The summation of all these voltages in a closed loop is equal to zero. Suppose n numbers of back to back connected elements form a closed loop. Among these circuit elements m number elements are voltage source and n - m number of elements drop voltagesuch as resistors.
The voltages of sources are V1, V2, V3,................... Vm.
And voltage drops across the resistors respectively, Vm + 1, Vm + 2, Vm + 3,..................... Vn.
As it is said that the voltage gain conventionally considered as positive, and voltage drops are considered as negative, the voltages along the closed loop are -
+ V1, + V2, + V3,................... + Vm, − Vm + 1, − Vm + 2, − Vm + 3,.....................− Vn.
Now according to Kirchhoff Voltage law, the summation of all these voltages results to zero.
That means, V1 + V2 + V3 + ................... + Vm − Vm + 1 − Vm + 2 − Vm + 3 + .....................− Vn = 0.
So accordingly Kirchhoff Second Law,       ∑V = 0.
Application of Kirchhoff's Laws to Circuits
The electric current distribution in various branches of a circuit can easily be found out by applying Kirchhoff Current law at different nodes or junction points in the circuit. After that Kirchhoff Voltage law is applied, each possible loop in the circuit generates algebraic equation for every loop. By solving all these equations, one can easily find out different unknown currents, voltages and resistances in the circuits.
Some Popular Conventions We Generally use During Applying KVL
1) The resistive drops in a loop due to electric current flowing in clockwise direction must be taken as positive drops.
2) The resistive drops in a loop due to electric current flowing in anti-clockwise direction must be taken as negative drops.
3) The battery emf causing electric current to flow in clockwise direction in a loop is considered as positive.
4) The battery emf causing electric current to flow in anti-clockwise direction is referred as negative

Coulomb's Law

It was first observed in 600 BC by Greek philosopher Thales of Miletus, if two bodies are charged with static electricity, they will either repulse or attract each other depending upon the nature of their charge. This was just an observation but he did not establish any mathematical relation for measuring the attraction or repulsion force between charged bodies. After many centuries, in 1785, Charles Augustin de Coulomb who is a French physicist, published the actual mathematical relation between two electrically charged bodies and derived an equation for repulsion or attraction force between them. This fundamental relation is most popularly known as Coulomb's law.

Statement of Coulomb’s Law

First Law

Like charge particles repel each other and unlike charge particles attract each other.

Second Law

The force of attraction or repulsion between two electrically charged particles is directly proportional to the magnitude of their charges and inversely proportional to the square of the distance between them.

Formulas of Coulomb’s Law

According to the Coulomb’s second law,

Where,

1. ‘F’ is the repulsion or attraction force between two charged bodies.
2. ‘Q1’ and ‘Q2’ are the electrical charged of the bodies.
3. ‘d’ is distance between the two charged particles.

1. ‘k’ is a constant that depends on the medium in which charged bodies are presented. In S.I. system, as well as M.K.S.A. system k=1/4πε. 

The value of ε0 = 8.854 X 10-12C2/Nm2.


Principle of Coulomb’s Law

Suppose if we have two charged bodies one is positively charged and one is negatively charged, then they will attract each other if they are kept at a certain distance from each other. Now if we increase the charge of one body keeping other unchanged, the attraction force is obviously increased. Similarly if we increase the charge of second body keeping first one unchanged, the attraction force between them is again increased. Hence, force between the charge bodies is proportional to the charge of either bodies or both.

Now, by keeping their charge fixed at Q1 and Q2 if you bring them nearer to each other the force between them increases and if you take them away from each other the force acting between them decreases. If the distance between the two charge bodies is d, it can be proved that the force acting on them is inversely proportional to d2.

This development of force is not same for all mediums. As we discussed in the above formulas, εr would change for various medium. So, depends on the medium, creation of force can be varied.

Limitation of Coulomb’s Law

1. Coulomb's Law  is valid, if the average number of solvent molecules between the two interesting charge particles should be large.

1. Coulomb's Law  is valid, if the point charges are at rest.
2. It is difficult to apply the coulomb's law when the charges are in arbitrary shape. Hence, we cannot determine the value of distance‘d’ between the charges when they are in arbitrary shape

OHM'S LAW

One the most important & fundamental laws of electronics is the ohms law. This law defines the relationships between current, voltage and resistance. A good way to understand ohms laws is an analogy with a domestic water system.

Thinking how? Let’s see:

Let’s start with the terms present in the definition:

• V = voltage: The easiest way to think of voltage is to call it potential. We know the potential is something which is very useful to do work. Imagine two tanks of water connected with a pipe. If one tank of water is placed higher than the other then there is potential for water to flow from the high level tank to the low level tank. This water pressure is similar to that used to drive electricity around a circuit, called the potential difference, this is measured in volts. This potential difference is provided by a battery or in the case of huge electricity a generator at the generating station.

• I = current: As the water flows through the pipe in a water system due to potential difference ,in the same way an electric current flows through a copper wire. So, current is simply the transfer of something from one place to another. The standard unit of electric current is one ampere that is the current produced by a one volt source in a circuit having a resistance of one ohm.

• R = resistance: Resistance meaning anything that opposes the flow of current. In this case of two tanks of water connected by a pipe, imagine resistance is formed by the pipe. As the pipe gets wider, more water flows & as the pipe gets narrower, less water flows. If there were no pipe between the two bodies of water, we can say there is infinite resistance. The unit by which electrical resistance is measured is Ohm & one ohm is equal to the current of one ampere which will flow when a voltage of one volt is applied.

Now that you got the concept ohm, volt and ampere, so now it’s the time to introduce you to the relationship in between them that is ohms law. The statement is, the electric current passing through a conductor is directly proportional to the potential difference across it, provided that the temperature remains constant. The constant of proportionality is the resistance of the conductor.

The definition above simply states that the current passing through a conductor increases if you increase the voltage.

So, we can say: V proportional to I

Thus, V = IR, Where , V = potential difference in volts (V)

I = current in amps (A) and

R = the constant of proportionality that is the resistance.