IMPORTANT THEOREMS, LAWS AND DEFINITIONS

1.Ohm´s law:

The ratio of potential difference (V) between any two points on a conductor to the current (I) flowing between them, is constant, provided the temperature of the conductor does not change.

                              In other words, V/I= constant or V/I= R

2.Kirchhoff´s law´s:

 a. Kirchhoff’s Point Law or Current Law (KCL)

In any electrical network, the algebraic sum of the currents meeting at a point (or junction) is zero.

                              i.e incoming currents = outgoing currents

 b. Kirchhoff’s Mesh Law or Voltage Law (KVL)

The algebraic sum of the products of currents and resistances in each of the conductors in any closed path (or mesh) in a network plus the algebraic sum of the e.m.fs. in that path is zero.

3.Super Position Theorem:

Hence, this theorem may be stated as follows :

In a network of linear resistances containing  than one generator (or source of e.m.f.), the current which flows at any point is the sum of all the currents which would flow at that point if each generator where considered separately and all the other generators replaced for the time being by resistances equal to their internal resistances.

4. Thevenin Theorem:

The current flowing through a load resistance RL connected across any two terminals A and B of a linear, active bilateral network is given by Voc || (Ri + RL) where Voc is the open-circuit voltage (i.e. voltage across the two terminals when RL is removed) and Ri is the internal resistance of the network as viewed back into the open-circuited network from terminals A and B with all voltage sources replaced by their internal resistance (if any) and current sources by infinite resistance.

5.Reciprocity Theorem:

It can be stated in the following manner :

In any linear bilateral network, if a source of e.m.f. E in any branch produces a current I in any other branch, then the same e.m.f. E acting in the second branch would produce the same current I in the first branch.

6.Compensation Theorem:

As applied to d.c. circuits, it may be stated in the following for ways :

(i) In its simplest form, this theorem asserts that any resistance R in a branch of a network in

which a current I is flowing can be replaced, for the purposes of calculations, by a voltage

equal to – IR.

                                     OR

(ii) If the resistance of any branch of network is changed from R to (R + ΔR) where the

current flowing originally is I, the change of current at any other place in the network

may be calculated by assuming that an e.m.f. – I. ΔR has been injected into the modified

branch while all other sources have their e.m.f.s. suppressed and are represented by their

internal resistances only.

7.Norton´s Theorem:

This theorem may be stated as follows :

(i) Any two-terminal active network containing voltage sources and resistance when viewed from its output terminals , is equivalent to a constant-current source and a parallel resistance. The constant current is equal to the current which would flow in a short-circuit placed across the terminals and parallel resistance is the resistance of the network when viewed from these open circuited terminals after all voltage and current sources have been removed and replaced by their internal resistances.

8.Maximum Power Transfer Theorem: 

A resistive load will abstract maximum power from a network when the load resistance is equal to the resistance of the network as viewed from the output terminals, with all energy sources removed leaving behind their internal resistances.

9.Joule´s Law of Electric Heating: 

The amount of work required to maintain a current of I amperes through a resistance of R ohm for t second is

                            W.D. = I2 Rt joules

10.Law´s of Electrostatics:

     a.First Law. Like charges of electricity repel each other, whereas unlike charges attract each other.

     b.Second Law. According to this law, the force exerted between two point charges (i) is  directly proportional to the product of their strengths (ii) is inversely proportional to the square of the distance between them.

        This law is known as Coulomb’s Law and can be expressed mathematically as :

                               F ∝ Q1Q2/d2 or

                               F = k Q1Q2/d2

11.Gauss Law:

This is the meaning of Gauss’s law which may be stated thus : the surface integral of the normal component of the electric intensity E over a closed surface is equal to 1/ε0 times the total charge inside it.

12.Breakdown Voltage and Dielectric Strength: 

The disruptive or breakdown voltage of an insulator is the minimum voltage required to break it down.

Dielectric strength of an insulator or dielectric medium is given by the maximum potential difference which a unit thickness of the medium can withstand without breaking down.

13.Law of  Magnetic Force:

By using a torsion balance, Coulomb found that the force between two magnetic poles placed in a medium is

(i) directly proportional to their pole strengths

(ii) inversely proportional to the square of the distance between them and

(iii) inversely proportional to the absolute permeability of the surrounding medium.

14.Weber and Ewing´s Molecular Theory:

This theory was first advanced by Weber in 1852 and was, later on, further developed by Ewing in 1890. The basic assumption of this theory is that molecules of all substances are inherently magnets in themselves, each having a N and S pole.

15.Faraday´s Law´s of Electromagnetic Induction:

    a.First Law. It states :

Whenever the magnetic flux linked with a circuit changes, an e.m.f. is always induced in it.

                             or

Whenever a conductor cuts magnetic flux, an e.m.f. is induced in that conductor.

    b.Second Law. It states :

 The magnitude of the induced e.m.f. is equal to the rate of change of flux-linkages.

16. Lenz Law:

The direction of the induced current may also be found by this law which was formulated by Lenz in 1835. This law states, in effect, that electromagnetically induced current always flows in such direction that the action of the magnetic field set up by it tends to oppose the very cause which produces it.

17.Transformer:

A transformer is a static or stationary piece of apparatus by means of which electric power in one circuit is transformed into electric power of the same frequency in another circuit. It can raise or lower the voltage in a circuit but with a corresponding decrease or increase in current.

18.Generator:

An electrical generator is a machine which converts mechanical energy (or power) in to electrical energy (or power).

19.Motor:

An electric motor is a machine which converts electric energy (or power) in to mechanical energy (or power). 

20.Electric Traction:

By electric traction is meant locomotion in which the driving (or tractive) force is obtained from electric motors. It is used in electric trains, tramcars, trolley buses and diesel-electric vehicles etc. Electric traction has many advantages as compared to other non-electrical systems of traction including steam traction.