Inductance · 电感
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| inductance/ɪnˈdʌktəns/ | 电感 | diàn gǎn |
| henries/ˈhenriz/ | 亨利 | hēng lì |
A coil resists changes to its own current — electrical inertia
- Try to switch a coil's current on suddenly and it fights back.
- Its own changing flux induces an EMF that opposes the change.
- This self-opposition is called inductance 电感.
- Think of it as electrical inertia: current in a coil doesn't like to change quickly.
线圈抗拒自身电流的变化——电学惯性
- 试着突然接通线圈的电流,它就往回抗拒。
- 它自己变化的通量感应出一个对抗变化的电动势。
- 这种自我对抗叫作电感。
- 把它想成电学惯性:线圈里的电流不喜欢快速改变。
The self-induced EMF
- A changing current makes a changing flux through the coil's own turns.
- By Faraday and Lenz, this induces a back-EMF: $\varepsilon = -L\dfrac{dI}{dt}$.
- $L$ is the inductance, measured in henries 亨利 (H).
- The faster you change the current, the harder the coil pushes back.
自感电动势
- 变化的电流使穿过线圈自身各匝的通量变化。
- 由法拉第和楞次,这感应出一个反电动势:$\varepsilon = -L\dfrac{dI}{dt}$。
- $L$ 是电感,以亨利(H)量度。
- 你改变电流越快,线圈往回推得越用力。
The self-induced EMF of an inductor is: · 电感的自感电动势为：
$\varepsilon = -L\,dI/dt$ — proportional to the rate of current change. · $\varepsilon = -L\,dI/dt$ — 与电流变化率成正比。
A $4\ \text{H}$ inductor's current changes at $2\ \text{A/s}$. Find the induced EMF magnitude (in V). · 一个$4\ \text{H}$电感的电流在$2\ \text{A/s}$内发生变化。求感应电动势的大小（单位V）。
$|\varepsilon| = L\,dI/dt = 4 \times 2 = 8\ \text{V}$.
The SI unit of inductance is the . · 电感的SI单位是。
Inductance · 电感 $L$ is measured in henries (H). · 电感$L$以亨利（H）为单位测量。
What sets the inductance
- Like capacitance, $L$ depends on geometry, not on the current.
- More turns, a bigger area, or a longer coil change $L$.
- A tightly wound solenoid with many turns has a large inductance.
- Add an iron core and $L$ grows much larger still.
什么决定电感
- 像电容一样,$L$ 取决于几何,不取决于电流。
- 更多匝数、更大面积或更长的线圈都改变 $L$。
- 匝数多、绕得紧的螺线管有很大的电感。
- 加一个铁芯,$L$ 会大得多。
Energy stored in the field
- Building up a current stores energy in the coil's magnetic field.
- The stored energy is $U = \tfrac12 L I^2$.
- Compare it with a capacitor's $\tfrac12 C V^2$ — the magnetic twin.
- Switch the current off suddenly and this energy has to go somewhere (often a spark).
储存在场中的能量
- 建立起电流把能量储存在线圈的磁场里。
- 储存的能量是 $U = \tfrac12 L I^2$。
- 把它与电容器的 $\tfrac12 C V^2$ 相比——磁学的孪生。
- 突然切断电流,这份能量必须去某个地方(常常是火花)。
Inductance opposes change · 电感对抗变化
A changing current in a coil induces a back-EMF proportional to how fast the current changes. · 线圈中变化的电流会感应出反电动势，其大小与电流变化率成正比。
The energy stored in an inductor carrying current $I$ is: · 载流$I$的电感储存的能量为：
$U = \tfrac12 LI^2$ — the magnetic twin of $\tfrac12 CV^2$. · $U = \tfrac12 LI^2$ — 它是$\tfrac12 CV^2$的磁场对应物。
The mirror image of a capacitor
- A capacitor opposes sudden changes in voltage.
- An inductor opposes sudden changes in current.
- A capacitor stores energy in an electric field; an inductor in a magnetic field.
- Together they are the two energy-storing circuit elements.
电容器的镜像
- 电容器对抗电压的突然变化。
- 电感器对抗电流的突然变化。
- 电容器把能量储存在电场里;电感器储存在磁场里。
- 两者一起是储能的两种电路元件。
With a steady, unchanging current, an ideal inductor behaves like an ordinary wire. · 在稳定、不变的电流下，理想电感表现得像普通导线。
$dI/dt = 0$ gives zero back-EMF, so it acts like a plain wire. · $dI/dt = 0$给出零反电动势，因此它表现得像普通导线。
Select all · 所有 true statements about an inductor. · 选择关于电感的所有正确陈述。
Opposes current change, stores ½LI², geometric L. Opposing voltage change is a capacitor. · 对抗电流变化，储存 ½LI²，几何决定的L。对抗电压变化是电容器的特性。
A coil has $L = 2\ \text{H}$ and its current changes at $3\ \text{A/s}$. Find the induced EMF.
- $|\varepsilon| = L\dfrac{dI}{dt} = 2 \times 3$.
- $|\varepsilon| = 6\ \text{V}$, opposing the change.
一个线圈 $L = 2\ \text{H}$,它的电流以 $3\ \text{A/s}$ 变化。求感应电动势。
- $|\varepsilon| = L\dfrac{dI}{dt} = 2 \times 3$。
- $|\varepsilon| = 6\ \text{V}$,对抗变化。
An inductor opposes a change in current, not the current itself. A steady current ($dI/dt = 0$) induces no back-EMF at all — the coil then behaves like an ordinary wire. It only fights while the current is changing.
电感器对抗电流的变化,不是电流本身。稳定的电流($dI/dt = 0$)完全不感应反电动势——那时线圈表现得像一根普通导线。它只在电流变化时抗拒。
Inductance $L$ (in henries) is a coil's electrical inertia: a changing current self-induces a back-EMF $\varepsilon = -L\,dI/dt$. It depends on geometry and stores energy $U = \tfrac12 LI^2$. An inductor opposes changes in current, the mirror of a capacitor opposing changes in voltage.
电感 $L$(以亨利计)是线圈的电学惯性:变化的电流自感出一个反电动势 $\varepsilon = -L\,dI/dt$。它取决于几何,并储存能量 $U = \tfrac12 LI^2$。电感器对抗电流的变化,是电容器对抗电压变化的镜像。