Reoccurring Error in RLC Series Circuit Problems.

[buildingblocs]

Hi All,

In doing some practice RLC series circuit question, I have been obtaining incorrect values for active and reactive power. The magnitudes I obtain are correct however the sign of the value is not. I have attributed this to obtaining an incorrect argument for the absolute power, or computing phasors incorrectly. I have attached an image of the reasoning behind my problem solving however I must be fundamentally wrong somewhere.

 

[Babadag]

S=V.I*=(V.ejα).(I.ejβ)*= (V.ejα).(I.e − jβ)= V.I.ej(α − β) = VIcos(α − β) + j.VIsin(α − β)
I*=conjugated electric current α=θv ; β=θv-θz ;α-β=θz
Then S=V^2/Z.ejθz