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Fu-Kwun Hwang
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Posts: 3085   « Embed this message on: March 14, 2011, 09:15:23 pm » posted from:Taipei,T\'ai-pei,Taiwan This is a simulation of AC powered RC circuit.
It can be used to study phase between voltage of capacitor $VR$, voltage of resistor $VR$and voltage of AC power supply $Vs$.  $V_{AC}=V_C+V_R$, $I(t)=\frac{V_R}{R}=\frac{V_{AC}-V_C}{R}=\frac{V_{AC}-Q/C}{R}$ $V_C(t)=\frac{Q}{C}$ $Q(t)=\int I\, dt$
The current $I$ and voltage $V_C$ are 90 degree out of phase.

The voltage $V_C$ in capacitor is proportional to charge $Q$,
However, change $Q$ need to be charged by current $I$. ( $Q=\int I\,dt$).
So current $I$ is leading charge $Q$ (90 degree earlier).
And voltage in resistor $V_R$ is proportional to current $I$.
Voltage in R ( $V_R$)is leading Voltage in capacitor( $V_C$)

The following simulation assume, $V_{AC}=V_o \sin\,(\omega\,t+\phi)$ $V_R=I\,R,\qquad V_C=\frac{Q}{C}=\frac{1}{C}\,\int I dt$

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