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# 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.