AC i-V relationship for R, L, and C. Source v S (t) = Asin w t. Resistive Load. V R and i R are in phase. Phasor representation: v S (t) =Asin w t = Acos( w t-90 ° )= A -90 °= V S (j w ). I S (j w ) =(A / R) -90 °.
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Source vS(t) =Asinwt
VR and iR are in phase
Phasor representation: vS(t) =Asinwt = Acos(wt-90°)= A -90°=VS(jw)
IS(jw) =(A / R)-90°
Impendence: complex number of resistance Z=VS(jw)/ IS(jw)=R
Generalized Ohm’s law VS(jw) = Z IS(jw)
Everything we learnt before applies for phasors with generalized ohm’s law
VC(jw)= A -90°
Notice the impedance of a capacitance decreases with increasing frequency
Phasor: VL(jw)=A -90°
Opposite to ZC, ZL increases with frequency
Ex. 4.16, p180