# AC circuit with a capacitor

Let alternating emf , e = eo sinωt

Instantaneous charge on the Capacitor

Q = CV

Q = C e0 sin ωt ,

$\displaystyle i=\frac{dQ}{dt}$

i= ω C e0cos ωt

$\displaystyle i=\frac{e_o}{\frac{1}{\omega C}}cos\omega t$

$\displaystyle i=\frac{e_o}{X_C}cos\omega t$

Where , $X_c = \frac{1}{\omega C}$ is known as capacitive reactance

i= i0 cos ωt

i= i0 sin (ωt + π/2)

Where , $\large i_o = \frac{e_o}{X_c}$

The following diagrams show graphical representation and phasor treatment of current and voltage illustrating the phase difference between them.

In capacitor voltage lags the current or the current leads the voltage by π/2