Vector Algebra | Vector Diagram
Before studying electrical engineering it is essential to know that angular relation between mainly voltage and current in a system. For understanding the relation between voltage and current we should first know definition of vector and go through vector algebra and vector diagram.
Definition of VectorThere are some quantities which have both magnitude and as well as their direction of action. This type of quantities is called vector quantity. This is how one can make basic definition of vector in very few words. The most basic concept of a vector is that, it is a representation of these type of quantities in both magnitude and direction. Whenever we represent any quantity it may have some direction of action. Suppose if we say, a force of 5 N, it does not complete the picture. We should always have to say the force in which direction, i.e. that 5 N force is in upward, downward or in any other directions. So the vector quantity must be represented with the magnetite as well as its direction. The direction of any quantity can be represented by measuring the angle formed by the direction of the quantity and a reference axis. Here in this vector diagram the vector OB has a magnitude of |Z| at an angle θ with reference axis ox. This may be resolved into two components at right angle to each other, say these are The conventional method of representing vector
Vector AlgebraNow we will discuss about vector algebra. For different calcuilation, vector must be expressed algebraically. In the vector diagram the vector Z is the resultant of vectorically adding its components X and Y. This vector may be written in vector algebra as Where, j indicates that the component Y is in perpendicular to component X. The x axis in the vector diagram is known as 'real' or 'in-phase' axis and the vertical y axis is called 'imaginary' or 'quadrature' axis. The symbol 'j' which is associated with the quadrature component Y, may be considered as an operator which rotates a vector anticlockwise through 90o. If a vector has to be rotated anticlockwise through 180o then the operator j has to perform its function twice and since the vector has reversed its sense then j.j or j2 = − 1
|Which implies, j = √||− 1|