Capacitors · 电容器
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| capacitor/kəˈpæsɪtə/ | 电容器 | diàn róng qì |
| capacitance/kəˈpæsɪtəns/ | 电容 | diàn róng |
| farad/ˈfæræd/ | 法拉 | fǎ lā |
The device that saves up charge and dumps it in a flash
- A camera flash charges quietly, then releases its energy in a blink.
- The part that stores that charge is a capacitor 电容器.
- It is just two conductors holding equal and opposite charge.
- Capacitors show up in every circuit, timer, and power supply.
那个把电荷攒起来、一瞬间倾泻的装置
- 相机闪光灯悄悄充电,然后一眨眼就释放能量。
- 储存那份电荷的部件就是电容器。
- 它只是两个持有等量异号电荷的导体。
- 电容器出现在每一个电路、计时器和电源里。
Capacitance = charge per volt
- Capacitance 电容 $C$ measures how much charge a capacitor holds per volt.
- $C = \dfrac{Q}{V}$, in farads 法拉 (1 F $= 1$ C/V).
- More charge for the same voltage means a bigger $C$.
- The two plates always carry $+Q$ and $-Q$ — equal and opposite.
电容 = 每伏的电荷
- 电容 $C$ 量度电容器每伏能持有多少电荷。
- $C = \dfrac{Q}{V}$,单位是法拉(1 F $= 1$ C/V)。
- 相同电压下电荷越多,$C$ 越大。
- 两块板始终带 $+Q$ 和 $-Q$——等量异号。
Charge a capacitor · 给电容器充电
Change the voltage and plate spacing and watch the stored charge and field respond. · 改变电压和极板间距，观察储存的电荷和电场如何响应。
Capacitance is defined as: · 电容的定义为：
$C = Q/V$, charge stored per volt, in farads. · $C = Q/V$，每伏特储存的电荷量，单位为法拉。
The SI unit of capacitance is the ____. · 电容的国际单位制单位是 ____。
1 farad $= 1$ C/V. · 1 法拉 $= 1$ C/V。
Geometry sets the capacitance
- For parallel plates: $C = \dfrac{\varepsilon_0 A}{d}$.
- Bigger plates (more area $A$) hold more charge — larger $C$.
- Closer plates (smaller gap $d$) hold more charge — larger $C$.
- $C$ depends on shape and size only, not on $Q$ or $V$.
几何决定电容
- 对平行板:$C = \dfrac{\varepsilon_0 A}{d}$。
- 更大的板(面积 $A$ 更大)持有更多电荷——$C$ 更大。
- 更近的板(间隙 $d$ 更小)持有更多电荷——$C$ 更大。
- $C$ 只取决于形状和大小,不取决于 $Q$ 或 $V$。
To increase a parallel-plate capacitor's capacitance you can: · 要增加平行板电容器的电容，你可以：
$C = \varepsilon_0 A/d$: a smaller gap $d$ raises $C$. Voltage does not change $C$. · $C = \varepsilon_0 A/d$：较小的间隙$d$提高$C$。电压不改变$C$。
The capacitance of a fixed pair of plates does not change when you raise the voltage. · 固定极板对的电容在你提高电压时不会改变。
$C$ depends on geometry only; higher $V$ just stores more $Q$. · $C$ 仅取决于几何形状；更高的 $V$ 只是储存更多 $Q$。
Energy stored
- Charging a capacitor stores energy in its field: $U = \tfrac12 C V^2$.
- Equivalent forms: $U = \tfrac12 QV = \dfrac{Q^2}{2C}$.
- The flash dumps this energy fast to make a bright pulse.
- Double the voltage and you store four times the energy.
储存的能量
- 给电容器充电把能量储存在它的场里:$U = \tfrac12 C V^2$。
- 等价形式:$U = \tfrac12 QV = \dfrac{Q^2}{2C}$。
- 闪光灯快速倾泻这份能量,产生明亮的脉冲。
- 电压加倍,你储存四倍的能量。
A $2\ \text{F}$ capacitor is charged to $3\ \text{V}$. Find the stored energy (in J). · 一个 $2\ \text{F}$ 电容器被充电至 $3\ \text{V}$。求储存的能量（单位：J）。
$U = \tfrac12 CV^2 = \tfrac12 (2)(3^2) = 9\ \text{J}$.
The field between the plates
- Between the plates the field is uniform: $E = \dfrac{V}{d}$.
- Push the plates closer (smaller $d$) and the same $V$ gives a stronger field.
- Too strong and the gap sparks — the capacitor's voltage limit.
- This uniform field is the parallel-plate picture from the fields unit.
板间的场
- 板之间的场是均匀的:$E = \dfrac{V}{d}$。
- 把板推得更近(更小的 $d$),相同的 $V$ 给出更强的场。
- 太强了间隙就打火——电容器的电压极限。
- 这个均匀场就是场单元里的平行板图像。
Select all · 所有 true statements about capacitors. · 选择关于电容器的 所有 正确陈述。
Equal/opposite charge, geometric C, energy ½CV². Raising V does not change C. · 等量/异号电荷，几何决定的 C，能量 ½CV²。升高 V 不改变 C。
Two plates of area $0.02\ \text{m}^2$ sit $1\ \text{mm}$ apart. Find $C$. ($\varepsilon_0 = 8.85\times10^{-12}$.)
- $C = \dfrac{\varepsilon_0 A}{d} = \dfrac{(8.85\times10^{-12})(0.02)}{0.001}$.
- $C \approx 1.8\times10^{-10}\ \text{F} = 180\ \text{pF}$.
两块面积 $0.02\ \text{m}^2$ 的板相距 $1\ \text{mm}$。求 $C$。($\varepsilon_0 = 8.85\times10^{-12}$。)
- $C = \dfrac{\varepsilon_0 A}{d} = \dfrac{(8.85\times10^{-12})(0.02)}{0.001}$。
- $C \approx 1.8\times10^{-10}\ \text{F} = 180\ \text{pF}$。
$C$ is set by geometry alone — area and gap. Raising the voltage does not change $C$; it just pushes proportionally more charge onto the same capacitor ($Q = CV$).
$C$ 只由几何决定——面积和间隙。提高电压不改变 $C$;它只是按比例把更多电荷推到同一个电容器上($Q = CV$)。
A capacitor stores equal and opposite charge on two plates: capacitance $C = Q/V$ (farads). For parallel plates $C = \varepsilon_0 A/d$ — geometry only. It stores energy $U = \tfrac12 CV^2$, with a uniform field $E = V/d$ between the plates.
电容器在两块板上储存等量异号电荷:电容 $C = Q/V$(法拉)。对平行板 $C = \varepsilon_0 A/d$——只由几何决定。它储存能量 $U = \tfrac12 CV^2$,板间是均匀场 $E = V/d$。