📚 AS Physics: Capacitance Key Points | AS 物理：电容 考点精讲
Capacitance is a fundamental concept in electricity that describes the ability of a system to store electric charge per unit potential difference. In AS Physics, you will learn the definition, formulas, energy storage, and behavior of capacitors in DC circuits, including charging and discharging through a resistor.
电容是电学中的一个基本概念，描述了系统在单位电势差下储存电荷的能力。在 AS 物理中，你将学习电容的定义、公式、能量储存以及电容器在直流电路中的行为，包括通过电阻充电和放电的过程。
1. Capacitance and Charge | 电容与电荷
Capacitance C is defined as the amount of charge Q stored per unit potential difference V across a capacitor: C = Q / V. The SI unit of capacitance is the farad (F). 1 F = 1 C V⁻¹. A capacitor of 1 farad stores 1 coulomb of charge when the potential difference across it is 1 volt.
电容 C 定义为电容器上每单位电势差 V 所储存的电荷量 Q：C = Q / V。电容的国际单位是法拉 (F)。1 F = 1 C V⁻¹。一个 1 法拉的电容在电势差为 1 伏特时可储存 1 库仑的电荷。
In practice, most capacitors have values in microfarads (µF), nanofarads (nF) or picofarads (pF). The charge stored is directly proportional to the applied voltage for a fixed capacitance, so the Q–V graph is a straight line through the origin with slope C.
实际中，大多数电容器的值在微法 (µF)、纳法 (nF) 或皮法 (pF) 数量级。对于固定电容，储存的电荷与外加电压成正比，因此 Q-V 图是一条过原点、斜率为 C 的直线。
2. Parallel Plate Capacitor | 平行板电容器
A simple capacitor consists of two parallel conducting plates separated by an insulator (dielectric). Its capacitance depends on the plate area A, separation d, and the permittivity ε of the dielectric material. The formula is: C = εA / d, where ε = ε₀εᵣ (ε₀ is the permittivity of free space, εᵣ is the relative permittivity or dielectric constant).
简单的电容器由两块平行导电板组成，中间夹有绝缘体（电介质）。其电容取决于板面积 A、间距 d 以及电介质材料的电容率 ε。公式为：C = εA / d，其中 ε = ε₀εᵣ（ε₀ 为真空电容率，εᵣ 为相对电容率或介电常数）。
Increasing the plate area or using a dielectric with higher εᵣ increases capacitance. Decreasing the separation d also increases capacitance. Note that d must be much smaller than the plate dimensions to avoid edge effects.
增加板面积或使用 εᵣ 更高的电介质可增加电容；减小间距 d 也能增加电容。注意为避免边缘效应，d 须远小于板尺寸。
3. Dielectrics and Relative Permittivity | 电介质与相对电容率
When a dielectric is inserted between the plates, it becomes polarised, reducing the effective electric field. This allows more charge to be stored for the same applied voltage, increasing capacitance. The relative permittivity εᵣ is the ratio of the capacitance with the dielectric to the capacitance in a vacuum: εᵣ = C / C₀.
当在极板间插入电介质时，介质会被极化，降低有效电场。这使得相同外加电压下能储存更多电荷，从而增加电容。相对电容率 εᵣ 是有电介质时的电容与真空时电容的比值：εᵣ = C / C₀。
Dielectrics also allow capacitors to operate at higher voltages without breakdown. Common dielectric materials include paper, ceramic, and electrolytic films.
电介质还能让电容器在更高电压下工作而不会击穿。常见的电介质材料包括纸、陶瓷和电解薄膜。
4. Energy Stored in a Capacitor | 电容器储存的能量
A charged capacitor stores electrical potential energy. The work done to charge the capacitor is given by the area under the Q–V graph, leading to the formulas: E = ½ QV = ½ CV² = ½ Q² / C. These equations are essential for solving problems involving capacitor discharge and energy conversion.
充电后的电容器储存电势能。给电容器充电所做的功等于 Q–V 图下的面积，从而得到公式：E = ½ QV = ½ CV² = ½ Q² / C。这些方程对于解决电容器放电和能量转换问题至关重要。
For a parallel plate capacitor, the energy can also be expressed in terms of the electric field E: energy density = ½ εE², where E = V/d. This shows that energy is stored in the electric field between the plates.
对于平行板电容器，能量也可用电场 E 表示：能量密度 = ½ εE²，其中 E = V/d。这表明能量储存在极板间的电场中。
5. Charging a Capacitor | 电容器的充电
When a capacitor is connected in series with a resistor and a DC voltage source, it does not charge instantly. The charge and voltage rise gradually following an exponential curve: V = V₀(1 – e-t/RC) and Q = Q₀(1 – e-t/RC) , where V₀ is the supply voltage, Q₀ = CV₀, and R is the resistance in the circuit.
当电容器与电阻和直流电源串联时，它不会立即充电。电荷和电压逐渐上升，遵循指数曲线： V = V₀(1 – e-t/RC) 和 Q = Q₀(1 – e-t/RC) ，其中 V₀ 为电源电压，Q₀ = CV₀，R 为电路中的电阻。
The charging current starts at a maximum value I₀ = V₀/R and decays exponentially to zero: I = I₀ e-t/RC . Initially the capacitor behaves like a short circuit; after a long time it behaves like an open circuit.
充电电流从最大值 I₀ = V₀/R 开始，指数衰减到零： I = I₀ e-t/RC 。初始时电容器如同短路；长时间后如同开路。
6. Discharging a Capacitor | 电容器的放电
When a charged capacitor is disconnected from the source and connected across a resistor, it discharges. The charge, voltage, and current all decay exponentially: V = V₀ e-t/RC , Q = Q₀ e-t/RC , and I = I₀ e-t/RC (with the current direction reversed compared to charging).
当充电的电容器与电源断开并连接到电阻两端时，电容器放电。电荷、电压和电流均按指数衰减： V = V₀ e-t/RC ， Q = Q₀ e-t/RC ， I = I₀ e-t/RC （电流方向与充电时相反）。
The discharge process is continuous; the time taken for the charge to halve is constant (t₁/₂ = RC ln 2 ≈ 0.693 RC).
放电过程是连续的；电荷减半所需的时间是恒定的 (t₁/₂ = RC ln 2 ≈ 0.693 RC)。
7. Time Constant and Exponential Decay | 时间常数与指数衰减
The time constant τ (tau) for an RC circuit is the product of resistance and capacitance: τ = RC. It represents the time for the charge (or voltage) to fall to 1/e (≈37%) of its initial value during discharge, or to rise to (1 – 1/e) (≈63%) of the final value during charging.
RC 电路的时间常数 τ = RC，表示在放电过程中电荷（或电压）下降至初始值的 1/e（约37%）所需的时间，或在充电过程中上升至最终值的（1 – 1/e）（约63%）所需的时间。
The time constant is measured in seconds (Ω × F =
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