Electrical Engineering ⇒ Topic : Phasor Representation of Sinusoidal Quantities

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 Y-axis 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 Y-axis at any instant gives the value of current at that instant. Thus when θ = 90⁰, the projection on Y-axis is OP (= I_m) itself. That the value of current at this instant (i.e. at θ or ωt = 90⁰) is I_m 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.

                                                              fig.(a)

The following points are worth noting :

• The length of the phasor represents the maximum value and the angle with axis of reference (i.e., X-axis) indicates the phase of the alternating quantity i.e. current in this case.
• The phasor representation enables us to quickly obtain the numerical values and, at the same time, have a picture before the eye of the events taking place in the circuit. Thus in the position of the phasor OP shown in Fig.(a), the instantaneous value is OM, the phase is θ and frequency is ω/2π.
• A phasor diagram permits addition and subtraction of alternating voltages or currents with a fair degree of ease.

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