It is sometimes helpful to treat the phase as if it defined a vector in a plane. The usual reference for zero phase is taken to be the positive x-axis and is associated with the resistor since the voltage and current associated with the resistor are in phase. The length of the phasor is proportional to the magnitude of the quantity represented, and its angle represents its phase relative to that of the current through the resistor. The phasor diagram for the RLC series circuit shows the main features.

In physics and engineering, a phase vector, or phasor, is a representation of a sine wave whose amplitude (A), phase (θ), and angular frequency (ω) are time-invariant. It is a subset of a more general concept called analytic representation. Phasors reduce the dependencies on these parameters to three independent factors, thereby simplifying certain kinds of calculations. In particular the frequency factor, which also includes the time-dependence of the sine wave, is often common to all the components of a linear combination of sine waves. Using phasors, it can be factored out, leaving just the static amplitude and phase information to be combined algebraically (rather than trigonometrically). Similarly, linear differential equations can be reduced to algebraic ones. The term phasor therefore often refers to just those two factors. In older texts, a phasor is also referred to as a sinor.

The rotating lines in the right hand part of the animation are a very simple case of a phasor diagram (named, I suppose, because it is a vector representation of phase). With respect to the x and y axes, radial vectors or phasors representing the current and the voltage across the resistance rotate with angular velocity ω. The lengths of these phasors represent the peak current Im and voltage Vm. The y components are Im sin (ωt) = i(t) and voltage Vm sin (ωt)= v(t). You can compare i(t) and v(t) in the animation with the vertical components of the phasors. The animation and phasor diagram here are simple, but they will become more useful when we consider components with different phases and with frequency dependent behaviour.

An AC circuit consists of a combination of circuitelements and an AC generator or source. The output of an AC generator is sinusoidal and varies with time according to the following equation.

In AC electrical theory every power source supplies a voltage that is either a sine wave of one particular frequency or can be considered as a sum of sine waves of differing frequencies. The neat thing about a sine wave such as V(t) = Asin(ωt + δ) is that it can be considered to be directly related to a vector of length A revolving in a circle with angular velocity ω - in fact just the y component of the vector. The phase constant δ is the starting angle at t = 0. In Figure 1, an animated GIF shows this relation [you may need to click on the image for it to animate]. 

1 comment:

  1. It's a nice post about phasor diagram. I like the way you have described it. It's really helpful. thanks for sharing it.