📚 IGCSE Edexcel Physics: Capacitance Key Points | IGCSE Edexcel 物理：电容 考点精讲
In IGCSE Edexcel Physics, capacitance is a topic that often appears in both Paper 1 and Paper 2. Understanding how capacitors store charge and energy is essential for solving circuit problems. This article summarises the key points you need to master for your exam.
在 IGCSE Edexcel 物理中，电容是试卷一和试卷二常见的考点。理解电容器如何存储电荷和能量对于解决电路问题至关重要。本文总结了你需要掌握的核心考点。
1. What is a Capacitor? | 什么是电容器？
A capacitor is an electrical component designed to store electric charge. It consists of two conducting plates separated by an insulating material called a dielectric. When connected to a voltage source, opposite charges build up on the plates, storing energy in the electric field between them.
电容器是一种用于存储电荷的电子元件。它由两片被绝缘材料（称为电介质）隔开的导电板组成。当连接到电压源时，两个极板上会积累相反的电荷，在极板间的电场中储存能量。
The circuit symbol for a capacitor is two parallel lines of equal length, representing the plates. In a schematic, it may be polarised (electrolytic) with a curved plate indicating the negative terminal, or non-polarised with two straight plates.
电容器的电路符号是两条等长的平行线，代表极板。在电路图中，它可以是极性的（电解电容），用弯曲的板表示负极，或是无极性的，用两条直线表示。
2. Capacitance Definition | 电容定义
Capacitance (C) is defined as the amount of charge stored per unit potential difference (voltage) across the capacitor. It measures how much charge a capacitor can hold for a given voltage.
电容（C）定义为电容器每单位电势差（电压）所存储的电荷量。它衡量电容器在给定电压下能容纳多少电荷。
The defining formula is:
C = Q / V
定义公式为：
C = Q / V
m this relationship, a larger capacitance means more charge is stored at the same voltage.
其中 C 是电容（法拉 F），Q 是电荷（库仑 C），V 是电压（伏特 V）。公式可变形为 Q = C V 或 V = Q / C。从这个关系可知，电容越大，在相同电压下存储的电荷就越多。
3. Units of Capacitance | 电容的单位
Because the farad is very large for typical capacitors, practical units are microfarads (µF), nanofarads (nF) and picofarads (pF).
电容的国际单位是法拉（F）。1 法拉等于 1 库仑每伏特（1 F = 1 C/V）。由于法拉在实际电容器中通常很大，常用单位有微法（µF）、纳法（nF）和皮法（pF）。
Conversions: 1 µ 1 pF = 10⁻¹² F. You must be comfortable converting between these prefixes in calculations.
换算关系：1 µF = 10⁻⁶ F，1 nF = 10⁻⁹ F，1 pF = 10⁻¹² F。在计算中你必须能熟练进行单位换算。
4. Energy Stored in a Capacitor | 电容器储存的能量
A charged capacitor stores electrical potential energy. The energy is not stored in the plates themselves but in the electric field between them. When discharged, this energy can be released.
充电后的电容器储存电势能。能量并非储存在极板本身，而是储存在极板之间的电场中。放电时，这些能量可以释放出来。
The energy (E) stored is given by two equivalent formulas:
E = ½ Q V
E = ½ C V²
储存的能量（E）由两个等效公式给出：
E = ½ Q V
E = ½ C V²
rging from 0 to V is ½ V, and work done = charge × average voltage, giving ½ Q V. Substituting Q = C V yields ½ C V².
其中 Q 是电荷（库仑），V 是电压（伏特），C 是电容（法拉）。这些公式源于充电过程中电压从 0 升至 V，平均电压为 ½ V，做功 = 电荷 × 平均电压，得到 ½ Q V。代入 Q = C V 得到 ½ C V²。
Example: A 1000 µF capacitor charged to 12 V stores energy E = ½ × 1000×10⁻⁶ × (12)² = 0.072 J.
例如：一个 1000 µF 的电容器充电到 12 V，储存能量 E = ½ × 1000×10⁻⁶ × 12² = 0.072 J。
5. Charging a Capacitor | 电容器充电
When a capacitor is connected in series with a resistor to a DC supply, the voltage across the capacitor (Vc) starts at zero and increases. Initially, the p.d. rises rapidly, but as it approaches the supply voltage, the rate of increase slows down. The charging current is maximum at the moment of connection and falls smoothly to zero.
当电容器与电阻串联接到直流电源时，电容器两端电压（Vc）起初为零，然后上升。开始时电压迅速上升，但随着接近电源电压，上升速率减慢。充电电流在接通瞬间最大，随后平稳降至零。
Graphs: The voltage– a curve that starts at zero and asymptotically approaches the supply voltage. The current– supply / R) and decays to zero. Both are exponential in shape but you are only required to describe the shape qualitatively.
图线：电压-时间图是从零开始并渐近趋近电源电压的曲线。电流-时间图从峰值（I = 电源电压 / R）开始衰减至零。两者均呈指数形，但你只需要定性描述形状。
6. Discharging a Capacitor | 电容器放电
When a charged capacitor is disconnected from the supply and connected across a resistor, it discharges. The voltage across the capacitor starts at its initial value and decays to zero. The discharge current flows in the opposite direction to the charging current and also decreases from an initial maximum to zero.
当已充电的电容器与电源断开，并连接到电阻上时，它会放电。电容器两端电压从初始值开始衰减至零。放电电流方向与充电电流相反，也从初始最大值逐渐降至零。
The graphs of voltage and current against time are similar: both start at a maximum and fall exponentially to zero. The discharge is initially rapid and then slows down. During discharge, the energy stored in the capacitor is converted into internal energy (heat) in the resistor.
电压和电流随时间变化的图线相似：均从最大值开始，指数衰减到零。放电起初很快，然后变慢。在放电过程中，电容器储存的能量转化为电阻的内能（热量）。
7. Solving Problems with C = Q/V and Energy | 运用 C = Q/V 及能量公式解题
Exam questions often ask you to calculate capacitance, charge, voltage, or energy. Always ensure units are consistent (farads, coulombs, volts, joules). Convert submultiples like µF to F.
考试题目常要求计算电容、电荷、电压或能量。务必确保单位一致（法拉、库仑、伏特、焦耳）。将微法等转换为法拉。
Worked example: A capacitor of 470 µF stores a charge of 0.0235 C. Calculate the voltage across it.
解题示例：一个 470 µF 的电容器存储了 0.0235 C 的电荷。计算它两端的电压。
Using V = Q / C: V = 0.0235 / (470 × 10⁻⁶) = 50 V.
利用 V = Q / C：V = 0.0235 / (470 × 10⁻⁶) = 50 V。
sk: Find the energy stored. E = ½ Q V = 0.5 × 0.0235 × 50 = 0.5875 J. Or using E = ½ C V².
另一常见题：求储存的能量。E = ½ Q V = 0.5 × 0.0235 × 50 = 0.5875 J。或使用 E = ½ C V²。
8. Uses of Capacitors | 电容器的用途
Capacitors have many applications: smoothing out voltage ripples in power supplies, in timing circuits, in camera flashes where a capacitor discharges quickly to produce a bright flash, and in defibrillators to deliver a controlled energy pulse.
电容器有许多应用：在电源中平滑电压纹波、定时电路、相机闪光灯中电容快速放电产生强光，以及在心脏除颤器中提供受控能量脉冲。
In the IGCSE context, you may be asked to recognise these uses and link them to energy storage and discharge.
在 IGCSE 背景下，可能会要求你识别这些用途并将其与能量存储和放电联系起来。
9. Common Mistakes and Tips | 常见错误与提示
Mistake 1: Confusing charge with current. Charge is stored on the plates; current is the flow of charge in the circuit.
错误 1：混淆电荷与电流。电荷存储在极板上；电流是电路中电荷的流动。
Mistake 2: Forgetting to square the voltage in the energy formula. E = ½ C V², not ½ C V.
错误 2：忘记在能量公式中对电压平方。E = ½ C V²，而不是 ½ C V。
Mistake 3: Unit errors, using µF without converting to farads.
错误 3：单位错误，使用 µF 而未转换为法拉。
Tip: When plotting or interpreting charging/discharging graphs, label axes clearly and describe the shape as “initially rapid, then gradually slowing down”.
提示：在绘制或解释充/放电图时，清楚标注坐标轴，并将形状描述为“起初迅速，然后逐渐变慢”。
10. Summary of Key Equations and Concepts | 核心方程与概念总结
ning of capacitance, the behaviour of voltage and current during charging and discharging. Use
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