JEE Main & Advanced Physics Alternating Current / प्रत्यावर्ती धारा Phase

Physical quantity which represents both the instantaneous value and direction of alternating quantity at any instant is called it's phase. It's a dimensionless quantity and it's unit is radian.

If an alternating quantity is expressed as \[X={{X}_{0}}\sin (\omega \,t\pm {{\varphi }_{0}})\] then the argument of \[\sin (\omega \,t+\varphi )\] is called it's phase. Where \[\omega t=\]instantaneous phase (changes with time) and \[{{\phi }_{0}}=\]initial phase (constant w.r.t. time)

Some important values

Nature of wave form	Wave form	r.m.s. value	average value	Form factor \[{{R}_{f}}=\frac{r.m.s.\,value}{Average value}\]	Peak factor \[{{R}_{p}}=\frac{Peak value }{r.m.s.\,value}\]
Sinusoidal		\[\frac{{{i}_{0}}}{\sqrt{2}}\]	\[\frac{2}{\pi }{{i}_{0}}\]	\[\frac{\pi }{2\sqrt{2}}=1.11\]	\[\sqrt{2}=1.41\]
Half wave rectified		\[\frac{{{i}_{0}}}{2}\]	\[\frac{{{i}_{0}}}{\pi }\]	\[\frac{\pi }{2}=1.57\]	2
Full wave rectified		\[\frac{{{i}_{0}}}{\sqrt{2}}\]	\[\frac{2{{i}_{0}}}{\pi }\]	\[\frac{\pi }{2\sqrt{2}}\]	\[\sqrt{2}\]
Square or Rectangular		\[{{i}_{0}}\]	\[{{i}_{0}}\]	1	1

(1) Phase difference (Phase constant) : The difference between the phases of currents and voltage is called phase difference. If alternating voltage and current are given by \[V={{V}_{0}}\sin (\omega \,t+{{\varphi }_{1}})\] and \[i={{i}_{0}}\sin (\omega \,t+{{\varphi }_{2}})\] then phase difference \[\phi ={{\phi }_{1}}-{{\phi }_{2}}\] (relative to current) or \[\varphi ={{\varphi }_{2}}-{{\varphi }_{1}}\] (relative to voltage)

(2) Time difference : If phase difference between alternating current and voltage is \[\phi \] then time difference between them is given as \[\text{T}\text{.D}\text{.}=\frac{T}{2\pi }\times \varphi \]

(3) Phasor diagram : A diagram representing alternating current and alternating voltage (of same frequency) as vectors (phasors) with the phase angle between them is called a phasor diagram.

While drawing phasor diagram for a pure element (e.g. R, L or C) either of the current or voltage can be plotted along X-axis. But when phasor diagram for a combination of elements is drawn then quantity which remains constant for the combination must be plotted along X-axis so we observe that

(i) In series circuits current has to be plotted along X-axis.

(ii) In parallel circuits voltage has to be plotted along X-axis.