AC source powered RC circuit

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 (math_failure (math_image_error): 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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