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IGCSE Physics: Capacitors - Key Concepts Review | IGCSE 物理：电容 考点精讲

2026-07-14 18:01 · 本文部分内容由AI辅助创作

📚 IGCSE Physics: Capacitors - Key Concepts Review | IGCSE 物理：电容 考点精讲

Capacitors are essential components in electrical circuits, widely used for storing electric charge and energy. Understanding capacitors is crucial for IGCSE Physics, as they appear in both the core and extended syllabus. This article provides a comprehensive revision of all key concepts related to capacitors, including capacitance, charging and discharging, energy storage, and practical applications.

电容器是电路中储存电荷和能量的重要元件。理解电容器对IGCSE物理至关重要，在核心与扩展大纲中均有所涉及。本文全面梳理电容相关考点，包括电容定义、充放电过程、能量储存及实际应用。

1. Introduction to Capacitors | 电容简介

A capacitor is a passive electronic component that stores electric charge and energy in an electric field. It can release this stored charge almost instantaneously, making it useful in timing, filtering, and energy‑storage applications.

电容器是一种无源电子元件，能在电场中储存电荷和能量。它几乎可以在瞬间释放所储存的电荷，因此在定时、滤波和储能应用中都很有用。

In its simplest form, a capacitor consists of two conductive plates separated by an insulating material called a dielectric. When a potential difference is applied across the plates, positive and negative charges accumulate on opposite plates, creating a uniform electric field.

最简单的电容器由两片导电板构成，中间被绝缘材料（介质）隔开。当在两极板间施加电势差时，正负电荷分别积聚在相对的极板上，产生匀强电场。

2. Capacitance: Definition and Formula | 电容：定义与公式

Capacitance (C) is defined as the ratio of the charge (Q) stored on either plate to the potential difference (V) across the capacitor. The defining formula is:

电容（C）定义为电容器任一极板所带电荷量（Q）与两极板间电势差（V）之比。定义公式为：

C = Q / V

Capacitance is measured in farads (F). A capacitor has a capacitance of 1 farad if 1 coulomb of charge produces a potential difference of 1 volt across it. In practice, farad is a very large unit, so smaller submultiples are used.

电容的单位是法拉（F）。若1库仑的电荷使电容器两端产生1伏特的电势差，则其电容为1法拉。实际中法拉是很大的单位，因此常用更小的分单位。

3. Units of Capacitance | 电容的单位

The SI unit of capacitance is the farad (F). Because 1 F is impractically large for most electronic components, we often use microfarads, nanofarads and picofarads. The conversions are shown in the table below.

电容的国际单位是法拉（F）。由于1法拉对大多数电子元件来说太大，我们通常使用微法、纳法和皮法。换算关系见下表。

UnitSymbolValue in farads
microfaradµF10⁻⁶ F
nanofaradnF10⁻⁹ F
picofaradpF10⁻¹² F

Always check the multiplier prefix when calculating charge or energy. For example, a 100 µF capacitor has a capacitance of 100 × 10⁻⁶ F = 1.0 × 10⁻⁴ F.

在计算电荷或能量时务必核对单位前缀。例如，一个100 µF的电容器的电容为100 × 10⁻⁶ F = 1.0 × 10⁻⁴ F。

4. Capacitor Construction and Circuit Symbol | 电容器的结构与电路符号

Fixed capacitors typically use metal foil plates with a paper or plastic dielectric. Electrolytic capacitors are polarised and can store more charge per unit volume, but they must be connected with the correct polarity.

固定电容器通常使用金属箔作为极板，以纸或塑料作为介质。电解电容器是有极性的，单位体积能储存更多电荷，但连接时必须注意正负极。

The circuit symbol for a general (non‑polarised) capacitor is two parallel lines of equal length, representing the two plates. For an electrolytic capacitor, one plate is drawn as a straight line (positive) and the other as a curved line (negative), often with a '+' sign.

一般（无极）电容器的电路符号是两条等长的平行线，代表两极板。电解电容器的符号中，一条直线表示正极，一条弯曲线表示负极，通常还标有“+”号。

In circuit diagrams, the symbol is labelled with the capacitance value, e.g. '10 µF'. Understanding the symbol helps when tracing current paths during charging and discharging experiments.

在电路图中，该符号旁标注电容值，如“10 µF”。理解符号有助于在充放电实验中分析电流路径。

5. Factors Affecting Capacitance | 影响电容的因素

The capacitance of a parallel‑plate capacitor depends on three physical factors: the overlapping plate area (A), the distance between the plates (d), and the permittivity of the dielectric material (ε). Qualitatively:

平行板电容器的电容取决于三个物理因素：极板的正对面积（A）、极板间距（d）以及介质的介电常数（ε）。定性关系如下：

= ε₀ εᵣ A / d, although IGCSE does not require its use, only a qualitative understanding.

这些关系可以综合为公式 C = ε₀ εᵣ A / d，但IGCSE考试不要求使用该公式，只需定性理解。

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6. Charging a Capacitor | 电容的充电过程

ntial difference across the capacitor is zero, so the circuit carries the maximum current.

当电容器与电阻串联后连接到直流电源时，开始充电。初始时刻（t=0），电容器两端电压为零，因此电路中的电流最大。

As charge accumulates on the plates, the voltage across the capacitor rises, opposing the supply voltage. This reduces the current. Ultimately, when the capacitor voltage equals the supply voltage, the net voltage in the loop becomes zero and the current stops completely.

随着电荷在极板上积累，电容器两端的电压上升，与电源电压相抗衡，导致电流减小。最终，当电容器电压等于电源电压时，回路净电压为零，电流完全停止。

The charging process is not linear; the rate of voltage rise is initially fast and then slows down as it approaches the supply value. The circuit requires a finite time to charge fully.

充电过程并非线性；电压上升的速率最初很快，随后逐渐减慢，趋近于电源电压。充满电需要一定的时间。

7. Discharging a Capacitor | 电容的放电过程

If a fully charged capacitor is disconnected from the supply and connected across a resistor, it discharges. At the start of discharge, the capacitor voltage equals its initial charged voltage, and the current is maximum in the opposite direction.

若将已充满电的电容器脱离电源并连接到电阻两端，它就放电。放电开始时，电容器电压等于初始充电电压，反向电流最大。

As the stored charge flows through the resistor, the voltage across the capacitor decreases. This causes the current to decrease as well. Both the voltage and current decay towards zero.

随着储存的电荷流过电阻，电容器两端电压下降，电流也随之减小。电压和电流均衰减至零。

Discharging is also non‑linear: the voltage drops quickly at first and then more gradually. The capacitor is considered fully discharged after a sufficiently long time.

放电也是非线性的：电压起初下降较快，然后逐渐变慢。经过足够长的时间后，电容器视为完全放电。

8. Voltage–Time Graphs and Time Constant | 电压-时间图像与时间常数

The way the capacitor voltage changes with time during charging and discharging follows an exponential law. Sketching and interpreting these graphs is an important IGCSE skill.

充电和放电过程中电容器电压随时间的变化遵循指数规律。绘制并解读这些图像是IGCSE的重要技能。

Charging graph: The voltage starts at 0 V, rises steeply at first, then curves off, approaching the supply voltage V₀ asymptotically. The gradient is directly proportional to the current.

充电图像：电压从0 V开始，起初快速上升，然后曲线趋于平缓，无限趋近于电源电压 V₀。曲线的斜率与电流成正比。

Discharging graph: The voltage starts at V₀ and decays exponentially towards zero. The gradient is negative and becomes less steep with time.

放电图像：电压从 V₀ 开始按指数衰减至零。斜率为负且随时间的推移而变得平缓。

The speed of the process is determined by the product of resistance (R) and capacitance (C). This product is called the time constant, represented by the Greek letter τ (tau):

充放电的快慢取决于电阻（R）和电容（C）的乘积。该乘积称为时间常数，用希腊字母 τ 表示：

τ = R × C

A larger τ means the capacitor takes longer to charge or discharge. For example, doubling either R or C doubles the time needed to reach a given fraction of the final voltage.

时间常数 τ 越大，充放电所需时间越长。例如，将 R 或 C 增加一倍，达到最终电压某一比例所需的时间也增加一倍。

9. Energy Stored in a Capacitor | 电容储存的能量

A charged capacitor stores energy in the electric field between its plates. The amount of energy depends on the capacitance and the voltage, given by:

充电的电容器将能量储存于极板间的电场中。能量的大小取决于电容和电压，公式如下：

E = ½ Q V = ½ C V² = ½ Q² / C

Because the voltage builds up from zero during charging, the average voltage during the process is V/2, which explains the factor ½.

由于充电过程中电压从零开始建立，过程中的平均电压为 V/2，因此公式中有因子 ½。

Worked example: A 470 µ ⁶ F × (6.0 V)² = 8.46×10⁻³ J. This energy can be released rapidly, e.g. in a camera flash.

计算示例：一个470 µF的电容器充电至6.0 V，储存的能量为 E = ½ × 470×10⁻⁶ F × (6.0 V)² = 8.46×10⁻³ J。该能量可快速释放，例如用于照相机闪光灯。

10. Practical Applications of Capacitors | 电容的实际应用

Capacitors are found in almost every electronic device. Common applications include:

电容器几乎出现在所有电子设备中。常见的应用有：