"Phasor in Circuit Elements"

Phasors allow us to express current-voltage relationships for inductors and capacitors much like we express the current-voltage relationship for a resistor.How to represent a voltage or current in the phasor or frequency domain, one may legitimately ask how we apply this to circuits involving the passive elements R, L, and C. What we need to do is to transform the voltage-current relationship from the time domain to the frequency domain for each element. Again, we will assume the passive sign convention.

We begin with the resistor. If the current through a resistor 

R is i = Im cos(ωt + φ),

 the voltage across it is given by Ohm’s law as 

v = iR = RIm cos(ωt + φ)

Figure representation: