Inductor

Unit

The unit of inductance $L$ is the henry (symbol: $H$), but it is too large for normal usage. So a more common unit is millihenrys, abbreviated as $mH$ ($1mH == 10^{-3}H$)

Inductor i-v equation

$v = L\frac{di}{dt}$

Feature

1. If a constant current flows in an inductor, then $\frac{dt}{di} = 0$ (a constant's derivative is 0), so in that case, there is zero voltage across the inductor.（Zero voltage means an inductor with constant current looks like a short circuit, the same as a plain wire.）

2. The current in an inductor does not (will not) change instantaneously.

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

So here we can see:

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

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

Actually, $wL$ is just like a resistor value $R$ in $U = RI$

So we call $wL$ inductive reactance (感抗). $\Omega$ is the unit of him.