📚 Capacitors in Use | 电容器的实际应用
Capacitors are not just textbook components that store charge on two metal plates. In A-level physics, understanding how capacitors behave in real circuits connects the exponential charge and discharge equations to practical devices such as power supplies, camera flashes, timing circuits, touchscreens and emergency backup systems.
电容器不仅仅是教科书中在两个金属极板上储存电荷的元件。在 A-level 物理中，理解电容器在实际电路中的行为，可以将指数充放电方程与电源、相机闪光灯、定时电路、触摸屏和应急备用系统等实际设备联系起来。
1. Capacitor Basics and Role in DC Circuits | 电容器基础与在直流电路中的作用
A capacitor of capacitance C stores charge Q when a potential difference V is applied across its plates. The charge stored is directly proportional to the p.d., giving C = Q/V. The work done in charging the capacitor is stored as electrical potential energy in the electric field between the plates, given by E = ½CV² = ½QV = ½Q²/C.
电容器的电容为 C，当两极板间施加电势差 V 时，储存的电荷量为 Q。储存的电荷量与电势差成正比，即 C = Q/V。充电过程中所做的功以电势能形式储存在极板间的电场中，其能量为 E = ½CV² = ½QV = ½Q²/C。
C = Q / V | E = ½ C V² = ½ Q V = ½ Q² / C
In a steady direct-current circuit, after the charging transient has finished, the capacitor behaves like an open circuit because no conduction current can flow through the dielectric. This blocking ability is useful when a circuit must separate DC bias from changing signals.
在稳定的直流电路中，充电暂态结束后，电容器相当于开路，因为介质中不能通过传导电流。当电路需要将直流偏置与变化信号分开时，这种隔直流能力非常有用。
2. Smoothing Rectified AC | 整流交流电的平滑滤波
A rectifier alone produces a unidirectional but rapidly changing voltage. When a capacitor is connected across the rectifier output and load, it charges to the peak e.m.f. during each conducting half-cycle and discharges through the load between peaks. If the discharge time constant CR is much larger than the period of the ripple, the output p.d. falls only slightly before the next peak recharges the capacitor.
单独的整流器输出的虽然是单向电压，但变化很快。当电容器并联在整流器输出端和负载两端时，它在每个导通的半周期内充电至峰值电动势，并在峰值之间通过负载放电。如果放电时间常数 CR 远大于纹波周期，则输出电压在下次峰值充电前只会略微下降。
For a full-wave rectified supply, the approximate peak-to-peak ripple voltage is V(ripple) ≈ I/(2fC), where I is the load current, f is the mains frequency and C is the smoothing capacitance. A larger capacitance or a smaller load current reduces the ripple.
对于全波整流电源，近似的峰峰值纹波电压为 V(ripple) ≈ I/(2fC)，其中 I 为负载电流，f 为市电频率，C 为滤波电容。增大电容或减小负载电流都可以减小纹波。
V(ripple) ≈ I / (2 f C)
| Rectifier type | 整流类型 | Ripple frequency | Approximate ripple p.d. |
|---|---|---|---|
| Full-wave | 全波 | 2f | V(ripple) ≈ I/(2fC) |
| Half-wave | 半波 | f | V(ripple) ≈ I/(fC) |
In a practical DC power supply, the smoothing capacitor is often an electrolytic capacitor with a capacitance of hundreds or thousands of microfarads. It works together with a voltage regulator to produce a nearly constant DC output.
在实际直流电源中，平滑滤波电容通常使用电容值为数百或数千微法的电解电容。它与稳压器配合工作，产生几乎恒定的直流输出。
3. Time Delay and Timing Circuits | 延时与定时电路
Capacitors are widely used to create time delays because the p.d. across a capacitor cannot change instantaneously. When a capacitor C charges through a resistor R from a supply of e.m.f. V₀, the p.d. across the capacitor rises according to V = V₀(1 − exp(−t/RC)). The product RC is called the time constant τ, and it determines the charging or discharging speed.
电容器广泛用于产生延时，因为电容器两端的电势差不能瞬间突变。当电容 C 通过电阻 R 从电动势为 V₀ 的电源充电时，电容两端的电势差按 V = V₀(1 − exp(−t/RC)) 上升。乘积 RC 称为时间常数 τ，它决定充放电的快慢。
τ = R C | V = V₀ (1 − exp(−t / RC))
In a timing circuit, a comparator or a transistor switch monitors the capacitor p.d. When it reaches a preset threshold V_th, the circuit changes state. The delay time is given by t = −RC ln(1 − V_th/V₀). This principle is used in staircase lights, car interior light delays and burglar alarm entry delays.
在定时电路中，比较器或三极管开关监测电容器两端的电势差。当它达到预设阈值 V_th 时，电路状态发生改变。延时时间为 t = −RC ln(1 − V_th/V₀)。这一原理用于楼梯灯、汽车车内灯延时和防盗报警器进入延时等场合。
If a charged capacitor discharges through a resistor, the p.d. falls as V = V₀ exp(−t/RC). The time taken to fall from V₀ to a threshold V_th is t = RC ln(V₀/V_th). Choosing a larger R or C gives a longer delay.
如果已充电的电容器通过电阻放电，其电势差按 V = V₀ exp(−t/RC) 下降。从 V₀ 降至阈值 V_th 所需的时间为 t = RC ln(V₀/V_th)。选择更大的 R 或 C 可获得更长的延时。
4. Camera Flash and Pulse Power | 相机闪光灯与脉冲功率
A camera flash unit uses a capacitor to deliver a very short but intense pulse of energy. Inside the flash circuit, a battery or a small oscillator charges a capacitor to a high voltage, often around 300 V. The energy stored is E = ½CV². When the flash is triggered, the capacitor discharges rapidly through a xenon tube, producing a bright flash of light.
相机闪光灯单元利用电容器提供极短但强度很高的能量脉冲。在闪光灯电路内部，电池或小型振荡器将电容器充电至高电压，通常约为 300 V。储存的能量为 E = ½CV²。触发闪光灯时，电容器通过氙灯管快速放电，产生明亮闪光。
E = ½ C V² | P = E / t
The charge may take several seconds, but the discharge can occur in a few milliseconds. This gives a very high pulse power P = E/t. For example, a capacitor storing 100 J that discharges in 2 ms delivers an average power of about 50 kW, even though the battery only supplies a few watts during charging.
充电可能需要几秒钟，但放电可在几毫秒内完成。这就产生了很高的脉冲功率 P = E/t。例如，一个储存 100 J 能量的电容器若在 2 ms 内放电，其平均功率约为 50 kW，而充电时电池只提供几瓦的功率。
5. Backup Power and Memory Protection | 备用电源与存储器保护
Small capacitors and supercapacitors can provide backup power for low-power digital circuits. In computers, capacitors across real-time clock chips or volatile memory can maintain the supply p.d. for a short time during a power interruption or while a battery is being replaced. This prevents loss of stored data.
小型电容器和超级电容器可为低功耗数字电路提供备用电源。在计算机中，实时时钟芯片或易失性存储器两端的电容器可以在断电或更换电池期间短时间维持电源电势差，从而防止存储数据丢失。
A supercapacitor, also called an electric double-layer capacitor, has a very large capacitance, sometimes thousands of farads. It stores energy E = ½CV² and can release it much faster than a battery, although its energy density is lower. This makes supercapacitors suitable for bridging short power gaps.
超级电容器也称为双电层电容器，其电容值非常大，有时可达数千法拉。它储存能量 E = ½CV²，并且可以比电池更快地释放能量，尽管其能量密度较低。这使超级电容器非常适合填补短时间的供电中断。
6. Coupling and Decoupling in Amplifiers | 放大器中的耦合与去耦
In amplifier circuits, capacitors are used for coupling and decoupling. A coupling capacitor passes an alternating signal from one amplifier stage to the next while blocking the DC bias voltage of one stage from affecting the next. The reactance of a capacitor is X_C = 1/(2πfC), so it offers a low impedance to high-frequency signals and a high impedance to low-frequency or DC signals.
在放大器电路中，电容器用于耦合和去耦。耦合电容将交流信号从一级放大器传递到下一级，同时阻止前级的直流偏置电压影响后级。电容的电抗为 X_C = 1/(2πfC)，因此它对高频信号呈现低阻抗，对低频或直流信号呈现高阻抗。
X_C = 1 / (2 π f C)
A decoupling capacitor is connected between a supply rail and ground. It provides a low-impedance path for high-frequency noise or sudden current spikes, keeping the supply voltage stable for integrated circuits. Without decoupling capacitors, digital circuits can malfunction due to switching noise.
去耦电容连接在电源轨与地之间。它为高频噪声或突发电流尖峰提供低阻抗通路，从而保持集成电路的供电电压稳定。如果没有去耦电容，数字电路可能因开关噪声而出现故障。
7. Tuning Circuits and Filters | 调谐电路与滤波器
Capacitors are essential in resonant circuits used for radio tuning and filtering. When a capacitor C is connected with an inductor L, the circuit can oscillate at its natural frequency. Resonance occurs when the capacitive reactance equals the inductive reactance, giving the resonant frequency f₀ = 1/(2π√(LC)).
电容器在用于无线电调谐和滤波的谐振电路中必不可少。当电容 C 与电感 L 连接时，电路可以在其固有频率下振荡。当容抗等于感抗时发生谐振，谐振频率为 f₀ = 1/(2π√(LC))。
f₀ = 1 / (2 π √(L C))
In a radio receiver, a variable capacitor changes the resonant frequency of the tuning circuit. When the circuit is tuned to the frequency of a particular station, the small alternating signal at that frequency produces the largest response, while signals at other frequencies are rejected. This is the basis of frequency selection in AM and FM radios.
在无线电接收机中，可变电容器改变调谐电路的谐振频率。当电路调谐到某个电台的频率时，该频率的小交流信号会产生最大响应，而其他频率的信号则被抑制。这就是调幅和调频收音机选频的基础。
8. Sensor Interfaces and Touchscreens | 传感器接口与触摸屏
The capacitance of a parallel-plate capacitor depends on plate area A, plate separation d and the dielectric material between the plates: C = ε₀εᵣA/d. Sensors can measure changes in capacitance caused by a change in distance, overlapping area or dielectric constant.
平行板电容器的电容取决于极板面积 A、极板间距 d 和极板间的介质材料：C = ε₀εᵣA/d。传感器可以通过测量电容的变化来检测距离、重叠面积或介电常数的变化。
C = ε₀ εᵣ A / d
Capacitive touchscreens use a grid of transparent electrodes. A finger placed near the screen changes the local capacitance because the human body acts as a conductor and a dielectric. The controller detects which electrode has changed and calculates the touch position. Capacitive sensors are also used for proximity detection, fluid level sensing and pressure measurement.
电容式触摸屏使用透明电极网格。手指靠近屏幕会改变局部电容，因为人体起到导体和介质的作用。控制器检测哪个电极发生了变化，并计算出触摸位置。电容式传感器还用于接近检测、液位传感和压力测量。
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