Capacitor

Unit

The unit of capacitance $C$ is the farad (symbol: $F$), but it is too large for normal usage. So a more common unit is microfarad, abbreviated as $\mu F$ ($1\mu F == 10^{-6}F$)

$$\begin{align*} u &= \sqrt{2} U \sin(wt + \psi_u) \\ \\ \\ i = C\frac{du}{dt} = C \cdot u^\prime &= \sqrt{2} wCU \cos(wt + \psi_u) = \sqrt{2}wCU \sin(wt + \psi_u + \frac{\pi}{2}) \\ \\ i &= \sqrt{2} I \sin(wt + \psi_u + \frac{\pi}{2}) = \sqrt{2} I \sin(wt + \psi_i) \end{align*}$$

So here we can see:

$$\begin{align*} I &= wCU \\ \\ \psi_i &= \psi_u + \frac{\pi}{2} \end{align*}$$

在电感元件中，电流的相位 $\psi_i$ 超前电压的相位 $\psi_u$ ${90}^\circ$

Actually, $\frac{1}{wC}$ is just like a resistor value $R$ in $I = \frac{U}{R}$

So we call $\frac{1}{wC}$ capacitive reactance (容抗). $\Omega$ is the unit of him.