In Fig OA represents a vector that is free to rotate anticlockwise about 0 at an angular velocity of w rad/s. A rotating vector is known as a phasor
After time t seconds the vector OA has turned through an angle w t. If the line BC is constructed perpendicular to OA as shown
, thenIf all such vertical components are projected on to a graph of y againstangle t (in radians), a sine curve results of maximum value OA. Any quantity which varies sinusoidally can thus be represented as a phasorA sine curve may not always start at 0°. To show this a periodic function is represented by y = sinwt + φ , where φ is the phase (or angle)difference compared with y = sin wt. In Figure y2 = sinwt + φ starts φ radians earlier than y1 = sin wt and is thus said to lead y1 by φ radians
In Figure y4 = sinwt - φ starts φ radians later than y3 =sin wt and is thus said to lag y3 byφ radians. Phasors y3 and y4 are shown in Figure
