what is phasor diagram, phasor algebra, leading & lagging ac quantities

Phasor diagram

A figure or diagram which gives the information (i.e. magnitude and phase angle) about alternating quantities known as phasor diagram or vector diagram.

Phasor Algebra

Any alternating voltage or current can be represented by vector , e.g.

A vector can be represented by two methods

(i) Rectangular representation

Vector can be represented in terms of X and Y components. As shown in the figure given below, vector E angle 0 can be represented by two components

‘j’ is used to indicate that Y component is perpendicular to X component. The value of

The representation A + j B is known as rectangular representation.

(ii) Polar representation

A vector E angle 0 is the polar representation. E is the magnitude and  is the angle with X-axis, clockwise for (—) ve value of and counter clockwise for (+) ve value of Polar representation can be converted to rectangular representation or vice-versa.

Addition and subtraction arc done in rectangular form.

e.g. (A +j B) + (C +j D) = (A + C) +j (B + D)

or (A +j B) – (C +j D) = (A + C) + j (B + D)

Multiplication and division is simpler in polar form

Leading and Lagging ac quantities

Leading ac quantities arc those which cover or attain its maximum value earlier or before as compared to other ac quantities on the time axis, whereas lagging ac quantities arc those which cover or attain its maximum value after or later as compared to other ac quantities.

As shown in above figure i.e. wave diagram and phasor diagram (i) v3 is leading with V1 by 60⁰ and is leading with v2 by 90⁰ .

(ii) V1 is lagging with v3 by 60⁰ and is leading with v2 by 30⁰ (iii) v2 is lagging with V1 by 30⁰ and is lagging with v3 by 90⁰.

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