INTER-RELATIONSHIP BETWEEN VARIOUS MATRICES

In this section,we will be discussing about the relationship between different matrices like incidence matrix(A),Tie-set matrix or Fundamental loop matrix(B) and Cut-set matrix(Q).

A=[A_t:A_l]  where, A_t means matrix of twigs and A_l  means matrix of links

B=[B_t:B_l] where , B_t means matrix of twigs and B_l means matrix of links

                 But for a fundamental loop matrix B_l =U,where U is the identity matrix.

Q=[Q_t:Q_l] where they have the usual meaning as stated above

RELATIONSHIP BETWEEN INCIDENCE MATRIX A AND FUNDAMENTAL LOOP MATRIX B:

We know that A and B are orthogonal.So

                                                   AB^T=0

[A_t:A_l]*B_t^T =0

              U

So A_tB_t^T+A_l=0   or    B_t^T=A_t^-1A_l

B_t= [ -A_t^-1 A_l ]^T

RELATIONSHIP BETWEEN A AND Q:

AI_b = 0     or      QI_b = 0

From this relation,we will get

Q_l = A_t^-1 A_l

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ARMATURE REACTION:

We know that an emf is induced in the coils of armature when there is a change in magnetic flux associated with it.So when there is no load connected to the armature, the current flowing through the armature winding is zero.Therefore the net magnetic flux of the system is created by the field system.

When there is a load connected to the armature winding the current flowing through the armature winding is non-zero value.So since there is a current flow through the winding,it causes generation of magnetic field and hence magnetic flux.Now the net magnetic flux get reduced since the magnetic flux created by armature winding either opposes or crosses perpendicularly to that produced by field system.

Any dc machine has two types of planes known as Magnetic Neutral Plane(MNP) and Geometric Neutral Plane(GNP).

The position of MNP and GNP are important on case of dc machine.GNP is always peerpendicular to the line connecting the centres of magnetic poles.Whereas MNP is always perpendicular to the resultant magnetic flux or mmf.

So when the load connected to armature winding is zero, resultant mmf is from north pole to south pole.So the MNP and GNP coincides.

But when a load is connected to armature winding,the net mmf rotates in a direction along the rotation of armature and hence there is a shift in MNP.Now MNP and GNP never coincides.

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Active Elements and Passive Elements

ACTIVE ELEMENTS

An independent source which can  deliver or absorb energy  continuously is called an active element . The voltage of an ideal source is assumed to be independent of the current in the circuit.

If the current is entering into the positive terminal of battery then power is absorbed by the battery and if the current is entering into the negative terminal of battery then power is delivered by the battery.                              

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Reciprocity Theorem or Reciprocal Theorem

RECIPROCAL THEOREM

A network is said to be reciprocal if the network remains invariant due to the interchange of position of cause and effect.

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Superposition Theorem

SUPERPOSITION  THEOREM

Superposition theorem states that for any linear network consisting of a number of sources,the overall response is equal to the algebraic sum of individual responses considering only one source at a time keeping all other sources inoperative.

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Thevenin's Theorem

THEVENIN’S THEOREM

Thevenin’s theorem states that for any two terminal linear network consisting of a number of sources can be replaced by a single voltage source in series with an impedance.

Thevenin’s voltage is the open circuit voltage across the terminals where we want to find Thevenin’s equivalent. Thevenin’s impedance is the net impedance across the terminals where we want to find the Thevenin’s equivalent.

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Sum of numbers using c program

In this tutorial we will discuss on how to find the sum of two numbers using c program.

For any c program the header file that must be included is stdio.h which stands for standard input output.

PROGRAM:

#include<stdio.h>

void main()

{

int a,b,sum;

printf(“Enter two numbers \n”);

scanf(“%d%d”,&a,&b);

sum=a+b;

printf(“Sum of two numbers is %d”,sum);

}

OUTPUT:

Enter two numbers

2 3

Sum of two numbers is 5

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