Electrical Engineering ⇒ Topic : Phasor Representation of Sinusoidal Quantities

Lalan
 
Phasor Representation of Sinusoidal Quantities Consider an alternating current represented by the equation i = I_{m} sin ωt. Take a line OP to represent to scale the maximum value I_{m}. 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 Yaxis is OM. OM = OP sin θ = I_{m} sin ωt = i, the value of current at that instant Hence the projection of the phasor OP on the Yaxis at any instant gives the value of current at that instant. Thus when θ = 90^{0}, the projection on Yaxis is OP (= I_{m}) itself. That the value of current at this instant (i.e. at θ or ωt = 90^{0}) is I_{m} can be readily established if we put θ = 90^{0} in the current equation. If we plot the projections of the phasor on the Yaxis versus its angular position pointbypoint, a sinusoidal alternating current wave is generated as shown in Fig (a). Thus the phasor represents the sine wave for every instant of time.
fig.(a) 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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