3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 111−+vR = RiR ZR^ =^ RiRiRvRt(a)(b)diLR vRdt−+vL = LdvC
iC = CdtZL = jωL1Direction of
rotation of phasorsTime Domain Phasors in Frequency DomainZC =iωCiL
iL vLL vL t(c)−+iC
iC
vC
C vC t−+IRVR IR−+ILVL−+ICZC VCZLZRICVL = ZLILVR = ZRIRVC = ZCICVLVCVRDirection of
rotation of phasors9090ILDirection of
rotation of phasorsFigure 3.1.1Voltage and current relationships in time domain and frequency domain for elementsR, L,
andC.(a)Current is in phase with voltage in a purely resistive circuit (unity power factor).(b)Current lags
voltage by 90° with a pure inductor (zero power factor lagging).(c)Current leads voltage by 90° with a pure
capacitor (zero power factor leading).
In constructing a phasor diagram, each sinusoidal voltage and current is represented by a
phasor of length equal to the rms value of the sinusoid, and with an angular displacement from
the positive real axis, which is the angle of the equivalent cosine function att=0. This use of the
cosine is arbitrary, and so also the use of the rms value. Formulation in terms of the sine function
could just as well have been chosen, and the amplitude rather than the rms value could have
been chosen for the magnitude. While phasor diagrams can be drawn to scale, they are usually
sketched as a visual check of the algebraic solution of a problem, especially since the KVL and
KCL equations can be shown as graphical addition.
Thereferenceof a phasor diagram is the lineθ=0. It is not really necessary that any voltage
or current phasor coincide with the reference, even though it is often more convenient for the