What is use of vector diagram | vector diagram definition | Application of vector diagram | Definition of scalar and vector quantity and phasor.

The most important concept for electrical engineer is What is use of vector diagram ? vector diagram is very use full concept for all electrical and electronic engineers.

Here we discus about its definition , application of vector diagram. some little over view on scalar quantity, vector quantity and phasor.

Vector diagrams are usually used with trigonometric functions.

Many electrical problems are solved through the use of trigonometry. The vector diagrams used with trigonometric functions are generally in the form of triangles and/or parallelograms.

Content :

👉 Definition of scalar and vector quantity and phasor
👉 Plotting a curve of alternating voltage
👉 Use of vector diagrams

Definition of scalar and vector quantity and phasor

Scalar quantity:

A scalar quantity is a quantity which is determined by the magnitude alone, for example energy, volume, temperature etc.

Vector quantity:

A vector quantity is a quantity which is represented by straight line with an arrow head to represent the magnitude and direction of it. For example, - force, velocity, weight

Phasor :

Phasor is a vector that is rotating at a constant angular velocity. A straight line with an arrow head is used to represent graphically the magnitude and phase of a sinusoidal alternating quantity (i.e. current, voltage and power) is called phasor.

Plotting a curve of alternating voltage:

If the maximum voltage of the alternator is known, the generated voltage can be plotted to form a curve. Draw a circle with the radius representing the maximum value of voltage. Any convenient scale may be used. Divide the circle into equal parts.

(Fig 1) Draw a horizontal line to scale, along which one voltage cycle will be plotted. Divide the line into the same number of equal parts as in the circle. Draw horizontal and vertical lines, as illustrated by the dashed lines in Fig 1.

The intersection of the lines represents the value of voltage at that instant.

For example, a horizontal and a vertical line intersect at point X.

Using the same scale as used for the radius of the circle, the value of voltage can be measured.

This value is the emf produced when the coil is cutting the lines of force at a 30-degree angle.

Use of vector diagrams:

The change which occurs in the value of an alternating voltage and/or current during a cycle can also be shown by using vector diagrams. A vector is a line segment that has a define length and direction. A vector diagram is two or more vectors joined together to convey information. Vector diagrams drawn to scale can be used to determine instantaneous values of current and/or voltage.

Fig 1 can be analyzed by means of vector diagrams according to the following procedure. Draw a horizontal line as a reference line (Fig 2).

Starting at point O and 30 degrees from the reference line, draw OA to scale to represent a maximum voltage (Vm) of 100 volts.

From the end of vector OA, draw a vertical dashed line is labelled AB and represents the instantaneous value of voltage (Vi) when the coil is cutting the lines of force at a 30 degree angle. Measure vector AB. It should scale to 50 volts.

The same procedure can be followed for any degree of rotation. The vector diagram shown in Fig 3 is used to determine the value of voltage when the coil has rotated 120 degrees.

Although the coil has rotated 120 degrees, the angle it is making with the lines of force is only 60 degrees. It is this angle that determines the value of the instantaneous voltage. For example, if the coil rotates 210 degrees, it cuts the lines of force at angle of 30 degrees.

Fig 4 Referring back to Fig 1, it can be seen that each division of the circle can represent vector OA. Vector AB can be represented by points along the voltage curve.

The angle between the horizontal diameter of the circle and the radius Vm is the angle at which the coil is cutting the flux. Although vector diagrams are seldom used alone, they are a simple way of presenting a visual illustration of a problem.

Vector diagrams are usually used with trigonometric functions.

Many electrical problems are solved through the use of trigonometry. The vector diagrams used with trigonometric functions are generally in the form of triangles and/or parallelograms.

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