Thursday, July 21, 2011

The equation of asinusoidal waveform

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

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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

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, 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

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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

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