> For the complete documentation index, see [llms.txt](https://yingshaoxo.gitbook.io/university-notes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://yingshaoxo.gitbook.io/university-notes/electrical-engineering/ac/ac-circuit.md).

# AC circuit

## What's the purpose of 3 basic components in AP circuit?

> If we need to block DC, we use a capacitor. 它具有充放电特性和阻止直流电流通过，允许交流电流通过的能力。
>
> If we need to block very high frequency AC, we use an inductor. 如果电感器在没有电流通过的状态下，电路接通时它将试图阻碍电流流过它；如果电感器在有电流通过的状态下，电路断开时它将试图维持电流不变。类似于稳(压)器。
>
> If we need to design a filter, we (can) use resistors, capacitors and inductors.

## As the previous

As far as I see, no matter in AC or DC, ohm's law is always useful:

$$
\dot U = \dot I \cdot R
$$

> 1

* But for different components, `R` is different.

  In Resistor, `R` is $$R$$

  In Inductor, `R` is $$wL$$

  In Capacitor, `R` is $$\frac{1}{wC}$$
* And of course, they becomes different in AC circuit with complex number(复数)

  $$R$$ becomes $$R$$

  $$wL$$ becomes $$jwL$$

  $$\frac{1}{wc}$$ becomes $$-j \cdot \frac{1}{wc}$$
* Don't ask me how these things come from, it's too complex for me to answer. Just remember it.

> 2

For each items, we no longer call them $$R$$, instead, we call them $$Z$$ (复阻抗)

如果几个`阻抗`通过`串`或`并`合在一起， we call them `复阻抗`

> 3

于是，和 DC analysis 一样，串联电阻相加，并联电阻$$\frac{(R1 \times R2)}{(R1+R2)}$$

只是运算上要注意很多事，比如:

$$
\begin{align\*}
&\frac{a\_1 \angle{b\_1}}{a\_2 \angle{b\_2}} = \frac{a\_1}{a\_2} \cdot \angle{(b\_1 - b\_2)}
\ \\
\&a\_1 \angle{b\_1} \times a\_2 \angle{b\_2} = a\_1 \cdot a\_2 \angle{(b\_1 + b\_2)}
\end{align\*}
$$

If you want to do some addition or subtraction, convert your equations to another 复数形式 first (like $$a + jb$$)

> 4 \* (not important)

如果得到的复阻抗，虚部为正，电感器起主导作用，整体电路呈感性

如果得到的复阻抗，虚部为负，电容器起主导作用，整体电路呈容性