Electrical Engineering ⇒ Topic : Phasor Representation of Sinusoidal Quantities
Phasor Representation of Sinusoidal Quantities
Consider an alternating current represented by the equation i = Im sin ωt. Take a line OP to represent to scale the maximum value Im. Imagine the line OP (or **phasor, as it is called) to be rotating in anticlockwise direction at an angular velocity (ω) rad/sec about the point O. Measuring the time from the instant when OP is horizontal, let OP rotate through an angle θ (= ωt) in the anticlockwise direction. The projection of OP on the Y-axis is OM.
OM = OP sin θ
= Im sin ωt
= i, the value of current at that instant
Hence the projection of the phasor OP on the Y-axis at any instant gives the value of current at that instant. Thus when θ = 900, the projection on Y-axis is OP (= Im) itself. That the value of current at this instant (i.e. at θ or ωt = 900) is Im can be readily established if we put θ = 900 in the current equation. If we plot the projections of the phasor on the Y-axis versus its angular position point-by-point, a sinusoidal alternating current wave is generated as shown in Fig (a). Thus the phasor represents the sine wave for every instant of time.
The following points are worth noting :
Note. Alternating voltages and currents are not vector quantities. Voltage is simply energy or work per coulomb and cannot be classified as a vector. Current is also not a vector quantity because it is merely the flow of electrons through a wire. When we insert an ammeter in a circuit to measure current or connect a voltmeter between two points to measure the potential difference (i.e. voltage), direction with reference to any set of axes is of no consequence. Therefore, neither alternating voltage nor current is a vector quantity. Instead, they are *phasors
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