A vector is a line that, through its length and also direction, to represent the magnitude and angle of application of a force or velocity or other vector quantity. ‘Phasor’ is a term supplied to describe rotating vectors which show up in electrical calculations. Voltage and current phasors represent the RMS value of the voltage or current by their length and the angle of the phase difference in between the phasor and the referral plane.

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Phasor Diagrams

Alternating currents and voltages, and their step relation, have the right to be stood for by way of sine waves, as in, Figures 1 (a), 2 (a) and 3 (a), but this method is inconvenient. A simpler method is to use phasors in a phasor diagram, as in Figures 1 (b), 2 (b) and 3 (b). Because the RMS worths of ac are of together importance, phasor diagrams are almost always scaled to stand for the RMS values and, uneven otherwise stated.


Figure 1 In-Phase electrical Phasors


Figure 2 Lagging electrical phasor


Figure 3 Leading electrical Phasor

Referring to Figure A, the referral phasor is always drawn horizontally and also to the right, and all phase angles should be measured native the referral phasor. When selecting the referral phasor, that is typical practice to select a amount that has actually the exact same value in all parts of the circuit.


Figure A electric Phasor Diagram

For a series circuit, the existing is provided as the referral phasor, because the current is usual to all parts of the circuit.

For a parallel circuit, the voltage is offered as the reference phasor, due to the fact that the voltage is common to all components of the circuit.

Later friend will view that transformers have a magnetic flux i m sorry is typical to the input and also output the the transformer, and so the flux i do not care the reference phasor.

Alternating currents result when an alternate voltage is applied throughout a load. As soon as the current and voltage curves pass with the zero place at the same time and increase to their maximum worths in the same direction, the wave creates are in phase through each other, as shown in Figures 1 (a). The phasor diagram for the in-phase condition is shown in Figure 1 (b).

A convention has actually been adopted in this publication to distinguish between voltage and also current phasors. The voltage phasor is drawn in red and the existing phasor is attracted in blue.

In some circuits, the current and also voltage curves execute not reach their zero and maximum worths simultaneously and they are claimed to it is in ‘out that phase’ and the angle of lead or lag is dubbed the ‘phase angle’ (symbol φ).

It should be detailed that this symbol is used by convention to suggest an angle between two phasors and is not interchangeable through the ‘theta’ (θ) symbol provided to suggest an angle of rotation. A second convention is that all phasors are assumed to rotate in one anticlockwise direction, beginning at the hopeful x-axis.

Figure 2 (a) shows the current lagging the voltage by 60° and Figure 2 (b) shows the same condition using phasors.

Figure 3 (a) shows the current leading the voltage through 60° and Figure 3 (b) shows the same condition using phasors.

Phasor enhancement by Graphical Method

Alternating worths of current or voltage can not be added arithmetically uneven they are in phase. If 2 AC voltages are linked in series, they could not be in phase with each other. One an approach of including phasors is to draw the phasors come scale and also angle, making use of RMS values, and also then add them together using the parallel method, as shown in Example 1 and Figure 4.


Figure 4 Parallelogram method

Example 1

Two voltages A and B are associated in series. Voltage A is 150 V and also leads the present by 45° voltage B is 100 V and lags the existing by 30°. Uncover the total EMF and also phase angle.

Since the two voltages space in series, the current is provided as the referral phasor. To build the phasor diagram, follow this steps: (Figure 4)

Step 1. attract the present phasor horizontally come the appropriate as the reference phasor.

Step 2. draw the phasors for VA and also VB to range measuring the phase angles from the referral phasor utilizing a protractor.

Step 3. build the phasor parallelogram.

Step 4. draw the resultant and also determine the complete EMF by scale and also measure the phase angle.

Total voltage = 201 V (ans A)

Phase angle Φ = 17° leading (ans B)

Phasor enhancement by mathematical Method

The graphical technique is helpful for estimating the complete value and often the is every the electric worker needs. But contemporary calculators do the task easy and far an ext accurate by the use of trigonometry and also many encompass a polar-to-rectangular converter role which girlfriend will quickly see as useful (even the iPhone has an app. For this!).

The calculation can be make using several methods, but the most common an approach uses trigonometry in a procedure that counter the polar-form phasors right into horizontal and also vertical components that are well-known as the rectangular form. Phasors in phase can be directly added together, for this reason the horizontal parts are included and so space the upright parts. The rectangular type that results is then converted back into a polar type phasor using Pythagoras’ theorem and the arc–tan (tan−1) function. This process is offered in Example 2 (a).

Some clinical calculators even have a duty to transform polar come rectangular and rectangular to polar, and also may even include the rectangular form, making the whole process quick and simple, as displayed in Example 2 (b).

Example 2

Two voltages A and B are associated in series. Voltage A is 150 V and leads the present by 45° voltage B is 100 V and also lags the existing by 30°.

(a)Find the total EMF and also phase angle by trigonometric method.


(b)Find the total EMF and phase angle making use of Polar to rectangular conversion (P>R) and also Rectangular to Polar counter (R>P) features on a an ideal calculator.

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Figure 5 shows the phasor diagram v the math supplied to identify each. This ends up fairly cluttered, therefore the phasor sketch is generally drawn at the peak of the calculation and the math is carry out under the diagram, as in Example 2.