电容器和电感器

Capacitors and Inductors

电容器和电容

A capacitor consists of two conducting plates separated by an insulator (or dielectric).

Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F).

$$q=Cv$$

or

$$C=\frac{\epsilon A}{d}$$

where $A$ is the area of the plates, $d$ is the distance between the plates, and ε is the dielectric constant of the material between the plates.

端口特性

$$\boxed{{\displaystyle i=C\frac{\mathrm{d}v}{\mathrm{d}t}}}$$

or

$$\boxed{{\displaystyle v(t)=\frac{1}{C}{\int }_{t_0}^{t}i(\tau )\mathrm{d}\tau +v(t_0)}}$$

储能

$$\boxed{{\displaystyle w=\frac{1}{2}C{v}^2}}$$

电感器和电感

An inductor consists of a coil of conducting wire.

Inductance is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H).

$$N\mathrm{\Phi }=Li$$

or

$$L=\frac{N^2\mu A}{l}$$

where N is the number of turns in the coil, μ is the permeability of the core, A is the cross-sectional area of the core, and ℓ is the length of the core.

端口特性

$$\boxed{{\displaystyle v=L\frac{\mathrm{d}i}{\mathrm{d}t}}}$$

or

$$\boxed{{\displaystyle i(t)=\frac{1}{L}{\int }_{t_0}^{t}v(\tau )\mathrm{d}\tau +i(t_0)}}$$

储能

$$\boxed{{\displaystyle w=\frac{1}{2}L{i}^2}}$$