📚 Capacitance | 电容
Capacitance is a fundamental concept in electricity that describes the ability of a system to store electric charge. In A-Level Physics, you will study how capacitors work, how to calculate their capacitance, and how they behave in DC circuits during charging and discharging. Understanding capacitance is essential for analysing energy storage, timing circuits, and many modern electronic applications.
电容是电学中一个基本概念，描述系统储存电荷的能力。在 A-Level 物理中，你将学习电容器如何工作、如何计算其电容，以及它们在直流电路中充放电时的行为。理解电容对于分析能量存储、定时电路和许多现代电子应用至关重要。
1. What is Capacitance? | 什么是电容？
Capacitance is the property of a component or circuit that enables it to store energy in the form of an electric field by accumulating electric charge. A device specifically designed to have capacitance is called a capacitor. It consists of two conducting plates separated by an insulating material known as a dielectric. When a voltage is applied across the plates, positive charge builds up on one plate and an equal amount of negative charge on the other, creating a potential difference.
电容是组件或电路通过积累电荷以电场形式储存能量的特性。专门设计用来提供电容的器件称为电容器。电容器由两块被绝缘材料（电介质）隔开的导电板组成。当在极板间施加电压时，正电荷在一块极板上积累，等量的负电荷在另一块极板上积累，从而产生电势差。
2. Definition and Unit: The Farad | 定义与单位：法拉
Capacitance C is defined as the ratio of the charge Q stored on either plate to the potential difference V between the plates:
C = Q / V
acitor has a capacitance of 1 F if a charge of 1 C raises its potential difference by 1 V.
电容 C 定义为每块极板上储存的电荷 Q 与极板间电势差 V 之比。单位是法拉 (F)，1 F = 1 C V⁻¹。若 1 C 的电荷使极板间电势差升高 1 V，则该电容器的电容为 1 F。
In practice, the farad is an extremely large unit. Most capacitors used in circuits have capacitances ranging from microfarads (µF, 10⁻⁶ F) to nanofarads (nF, 10⁻⁹ F) and picofarads (pF, 10⁻¹² F). These smaller units are far more common in electronics.
实际上，法拉是一个非常大的单位。电路中常用的电容器电容值通常在微法 (µF, 10⁻⁶ F) 到纳法 (nF, 10⁻⁹ F) 和皮法 (pF, 10⁻¹² F) 范围内。这些较小单位在电子学中更为常见。
3. The Parallel Plate Capacitor | 平行板电容器
The simplest capacitor geometry is the parallel plate capacitor: two flat, parallel conducting plates each of area A, separated by a small distance d. In a vacuum, its capacitance is given by
C = ε₀ A / d
¹² F m⁻¹. From this equation, we can see that capacitance increases with larger plate area A and decreases with larger separation d.
最简单的电容器几何形状是平行板电容器：两块面积为 A 的平行平面导电板，间距很小 d。在真空中，其电容为 C = ε₀ A / d，其中 ε₀ 是真空介电常数，ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹。由此可知，电容随板面积增大而增大，随间距增大而减小。
The physical reason is that a larger area allows more charge to accumulate for the same voltage, and a smaller separation produces a stronger electric field, increasing the capacity to store charge. These relationships are crucial when designing or analysing capacitors.
物理原因是，较大的面积允许在相同电压下积累更多电荷，较小的间距产生更强的电场，从而增加储存电荷的能力。这些关系在设计或分析电容器时至关重要。
4. Dielectrics and Relative Permittivity | 电介质与相对介电常数
When an insulating dielectric material is inserted between the plates, the capacitance increases by a factor called the relative permittivity (or dielectric constant) εr. The new capacitance becomes
C = εr ε₀ A / d
εr is dimensionless and depends on the material; for a vacuum εr = 1, for air εr ≈ 1.0006, for paper εr ≈ 3.7, and for distilled water εr cal benefit: it increases the breakdown voltage, allowing the capacitor to operate safely at higher voltages.
当在两板间插入绝缘介电材料时，电容会增大，增大的倍数称为相对介电常数 εr。新的电容为 C = εr ε₀ A / d。εr 是无量纲量，取决于材料；真空 εr = 1，空气 εr ≈ 1.0006，纸 εr ≈ 3.7，蒸馏水 εr ≈ 80。介电材料还有实际好处：它提高了击穿电压，使电容器能在更高电压下安全工作。
The microscopic explanation is that the dielectric becomes polarized in the electric field, producing an opposing field that reduces the net electric field between the plates. To maintain the same potential difference, more charge must be supplied, thus increasing capacitance.
微观解释是，介电材料在电场中被极化，产生一个抵消外场的内部电场，减弱了极板间的净电场。为维持相同的电势差，必须提供更多的电荷，因此电容增加。
5. Energy Stored by a Capacitor | 电容器储存的能量
A charged capacitor stores electrical potential energy in the electric field between its plates. The energy W required to charge a capacitor from uncharged to a final voltage V with charge Q is
W = ½ Q V = ½ C V² = ½ Q² / C
These three forms are all equivalent because of the relation C = Q / V. Energy is measured in joules (J).
带电的电容器在其极板间的电场中储存电势能。将一个未充电的电容器充电至最终电压 V、带电荷 Q 所需的能量 W 为 W = ½ Q V = ½ C V² = Q²/(2C)。这三种形式等价，因为 C = Q/V。能量单位是焦耳 (J)。
This stored energy can be released rapidly, as in a camera flash unit, where a capacitor discharges through a xenon tube to produce a brief, intense light. In defibrillators, a carefully calibrated capacitor discharges energy through the patient's chest to restore normal heart rhythm.
这种储存的能量可以迅速释放，例如在相机闪光灯中，电容器通过氙气灯管放电，产生短暂而强烈的光。在除颤器中，经过精确校准的电容器通过患者胸部释放能量，以恢复正常心律。
6. Charging a Capacitor through a Resistor | 通过电阻对电容器充电
When an initially uncharged capacitor is connected in series with a resistor to a DC voltage source, it does not charge instantly. The charge on the plates builds up gradually, and the voltage across the capacitor approaches the source voltage exponentially. The charge as a function of time t is given by
Q = Q₀ (1 − e−t/τ)
where Q₀ = C V₀ is the maximum charge when fully charged, and τ = RC is the time constant. The voltage across the capacitor follows V = V₀ (1 − e−t/τ).
当一个初始未充电的电容器与一个电阻串联连接到直流电源时，它并非立即充电。极板上的电荷逐渐积累，电容器两端的电压以指数方式趋近电源电压。电荷随时间 t 的变化为 Q = Q₀ (1 − e−t/τ)，其中 Q₀ = C V₀ 是完全充电时的最大电荷，τ = RC 是时间常数。电容器电压遵循 V = V₀ (1 − e−t/τ)。
The charging current initially is at its maximum I₀ = V₀ / R and then decays exponentially: I = I₀ e−t/τ. The decreasing rate of charge accumulation is because the growing voltage on the capacitor opposes the source voltage, reducing the net driving potential difference.
充电电流初始最大，为 I₀ = V₀ / R，然后以指数方式衰减：I = I₀ e−t/τ。电荷积累速率降低的原因是电容器上逐渐升高的电压与电源电压相对抗，减小了有效的驱动电势差。
Published by TutorHao | A-Level Physics Revision Series | aleveler.com更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图