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