📚 Alternating Voltages | 交流电压
An alternating voltage is an electromotive force (e.m.f.) whose polarity reverses periodically with time. Unlike a direct voltage, which maintains a steady direction, an alternating voltage continuously changes direction, typically following a sinusoidal pattern. This characteristic allows alternating voltages to be easily stepped up or down using transformers, making them ideal for long‑distance power transmission and household electricity supply worldwide.
交流电压是一种极性随时间周期性反转的电动势（e.m.f.）。与方向恒定的直流电压不同，交流电压不断改变方向，通常遵循正弦规律。这一特点使得交流电压可以方便地通过变压器升压或降压，非常适合远距离输电和全球家用电力供应。
1. Introduction to Alternating Voltages | 交流电压简介
rence varying sinusoidally with time. The instantaneous voltage can be described mathematically as V = V₀ sin(ωt), where V₀ is the peak voltage, ω is the angular frequency, and t is time. In the UK, the mains supply provides a root-mean-square voltage of about 230 V at a frequency of 50 Hz.
交流电压由交流发电机或电网等电源产生，提供随时间正弦变化的电位差。瞬时电压可用数学式 V = V₀ sin(ωt) 描述，其中 V₀ 为峰值电压，ω 为角频率，t 为时间。在英国，市电提供的均方根电压约为 230 V，频率为 50 Hz。
Alternating voltages are central to modern electrical engineering because they can be transformed efficiently and allow the use of induction motors and other a.c. machinery. The periodic reversal of current also helps in reducing electrochemical corrosion in certain applications.
交流电压在现代电气工程中居于核心地位，因为它能高效变压，并可用在感应电机等交流设备中。电流的周期性反转也有助于在某些应用中减轻电化学腐蚀。
2. Sinusoidal Waveform | 正弦波形
t), where f is the frequency in hertz and ω = 2πf. The sine function describes a smooth, repetitive oscillation that rises to a positive maximum, crosses zero, reaches a negative minimum, and returns to zero.
最常见的交流电压形式是正弦波。数学上，任意时刻的电压由 V = V₀ sin(2πft) = V₀ sin(ωt) 给出，其中 f 是以赫兹为单位的频率，ω = 2πf。正弦函数描绘了一种平滑、重复的振荡：上升到正最大值，穿过零点，到达负最小值，再回到零点。
V = V₀ sin(ωt)
V = V₀ sin(ωt)
A sinusoidal voltage is preferred for power distribution because it produces a rotating magnetic field in a.c. motors and causes less electromagnetic interference compared to other waveforms. Any periodic waveform can be built from a sum of sine waves (Fourier analysis), but the pure sinusoid gives the simplest and most efficient energy transfer.
正弦电压在配电中备受青睐，因为它能在交流电机中产生旋转磁场，且相比其他波形产生的电磁干扰较小。任何周期波形都可用正弦波之和构建（傅里叶分析），但纯正弦波实现最简单、能量传递最高效。
3. Key Parameters: Peak, Peak‑to‑Peak, Period and Frequency | 关键参数：峰值、峰峰值、周期和频率
voltage V₀ (or amplitude) is the maximum instantaneous value in either direction. The peak‑to‑ or one complete cycle, and the frequency f is the number of cycles per second, so f = 1/T.
分析交流电压时，几个参数必不可少。峰值电压 V₀（或称振幅）是任一方向上的最大瞬时值。峰峰值电压是从正峰值到负峰值的总电压摆幅，即 Vₚₚ = 2V₀。周期 T 是完成一个完整循环所需的时间，频率 f 是每秒的循环次数，因此 f = 1/T。
Vₚₚ = 2V₀, f = 1/T, ω = 2πf
Vₚₚ = 2V₀, f = 1/T, ω = 2πf
On an oscilloscope, the horizontal scale (time‑base) gives the period T, while the vertical scale (volts/div) gives the peak‑to‑peak voltage. These readings are fundamental for calculating other quantities like rms voltage and power.
在示波器上，水平标度（时基）给出周期 T，垂直标度（伏/格）给出峰峰值电压。这些读数是计算均方根电压和功率等其他量的基础。
4. Root Mean Square (RMS) Voltage | 均方根电压
sinusoidal waveform, the rms voltage Vᵣₘₛ is related to the peak voltage V₀ by Vᵣₘₛ = V₀ / √2. The derivation involves squaring the instantaneous voltage, taking the mean over one cycle, and then the square root of that mean.
交流电源的均方根电压是能在一个电阻上提供相同平均功率的直流电压值。对于正弦波形，均方根电压 Vᵣₘₛ 与峰值电压 V₀ 的关系为 Vᵣₘₛ = V₀ / √2。推导过程包括将瞬时电压平方、取一个周期内的平均值，再求该平均值的平方根。
Vᵣₘₛ = V₀ / √2 ≈ 0.707 V₀
Vᵣₘₛ = V₀ / √2 ≈ 0.707 V₀
ve heating capability of the a.c. supply. In the UK, the declared rms mains voltage is 230 V, which corresponds to a peak voltage of about 325 V (230 V × √2). Multimeters set to a.c. mode usually display the rms value.
由于负值的平方为正，均方根电压始终为正，代表交流电源的有效加热能力。在英国，标称市电均方根电压为 230 V，对应峰值电压约 325 V（230 V × √2）。调至交流档的万用表通常显示均方根值。
5. RMS Current and Power | 均方根电流与功率
Just as with voltage, an alternating current has an rms value Iᵣₘₛ = I₀ / √2 Iᵣₘₛ² R = Vᵣₘₛ² / R. These formulas mirror those for d.c. circuits but use rms quantities.
正如电压那样，交流电流也有均方根值 Iᵣₘₛ = I₀ / √2，其中 I₀ 为峰值电流。当交流电压 Vᵣₘₛ 加在电阻 R 两端时，耗散的平均功率为 P = Iᵣₘₛ Vᵣₘₛ = Iᵣₘₛ² R = Vᵣₘₛ² / R。这些公式与直流电路的公式相似，但使用的是均方根量。
For purely resistive loads, the current and voltage are in phase; hence the power factor is 1. For reactive components like inductors and capacitors, the power calculation involves a phase angle, but the rms values of voltage and current are still key to determining the apparent power.
对于纯电阻负载，电流与电压同相，因此功率因数为 1。对于电感器和电容器等电抗元件，功率计算涉及相位角，但电压和电流的均方根值仍然是决定视在功率的关键。
6. Half‑Wave Rectification | 半波整流
Half‑wave rectification converts an alternating voltage into a fluctuating direct voltage by allowing current to pass only during one half of each cycle. A single diode is placed in series with the load. During the positive half‑cycle, the diode conducts, and the output voltage follows the input; during the negative half‑cycle, the diode blocks, and the output is zero.
半波整流通过只让电流在每个周期的半个周期内通过，将交流电压转换为脉动直流电压。单个二极管与负载串联。正半周期间，二极管导通，输出电压跟随输入；负半周期间，二极管截止，输出为零。
The resulting output is a series of positive half‑sine pulses. The average d.c. voltage (mean value) for a sinusoidal input of peak V₀ is Vdc = V₀ / π. The rms output voltage of the half‑wave rectified signal is V₀ / 2. Half‑ simple but inefficient, as it uses only half the input cycle and has a high ripple factor.
输出为一连串正半正弦脉冲。对于峰值为 V₀ 的正弦输入，平均直流电压（均值）为 Vdc = V₀ / π。半波整流信号的均方根输出电压为 V₀ / 2。半波整流结构简单但效率低，因为它仅利用输入周期的半个部分，且纹波因数高。
7. Full‑Wave Rectification | 全波整流
Full‑wave rectification makes use of both half‑cycles of the alternating input. A bridge rectifier, consisting of four diodes arranged in a diamond configuration, directs the current through the load in the same direction regardless of the input polarity. During the positive half‑cycle, two diodes conduct; during the negative half‑cycle, the other two conduct. The output is a series of positive half‑sine waves at twice the input frequency.
全波整流利用交流输入的整个周期。由四只二极管按桥式排列组成的桥式整流器，无论输入极性如何，都能使电流以相同方向流过负载。正半周期间，两只二极管导通；负半周期间，另外两只导通。输出为一连串频率两倍于输入的正半正弦波。
The average d.c. voltage for a full‑wave rectified sine wave is Vdc = 2V₀ / π, which is double that of half‑wave rectification. The rms output voltage remains V₀ / √2, the same as the original a.c. supply. Full‑wave rectification is more efficient and easier to smooth, making it the standard for d.c. power supplies.
全波整流正弦波的平均直流电压为 Vdc = 2V₀ / π，是半波整流的二倍。输出均方根电压仍为 V₀ / √2，与原始交流电源相同。全波整流效率更高、更易于滤波，因而是直流电源的标准配置。
8. Smoothing with Capacitors | 电容滤波
The pulsating d.c. from a rectifier is unsuitable for sensitive electronic circuits, so smoothing is required. A large‑value capacitor is connected in parallel with the load. The capacitor charges to the peak voltage during the rising portion of the rectified pulse and discharges through the load resistor when the pulse falls, maintaining the output voltage between peaks.
整流器输出的脉动直流不适合灵敏的电子电路，因此需要滤波。大容量电容与负载并联。电容在整流脉冲上升段充电至峰值电压，当脉冲下降时通过负载电阻放电，从而在峰间维持输出电压。
The variation in output voltage is called ripple. For a full‑wave rectifier operating at mains frequency f, the ripple voltage Vripple is approximately Vripple and C is the capacitance. A larger capacitance reduces ripple, producing a smoother d.c. output. Additional filtering using inductors or voltage regulators can further stabilise the voltage.
输出电压的变化称为纹波。对于工作于市电频率 f 的全波整流器，纹波电压近似为 Vripple ≈ I / (2fC)，其中 I 为负载电流，C 为电容值。电容越大，纹波越小，输出直流更平滑。使用电感或稳压器进行额外滤波可以进一步稳定电压。
9. Transformer and Alternating Voltage | 变压器与交流电压
A transformer operates exclusively on alternating voltage. It consists of two coils wound on a common iron core. An alternating current in the primary coil creates a changing magnetic flux, which induces an alternating e.m.f. in the secondary coil. The ratio of the secondary voltage Vs to the primary voltage Vp equals the ratio of the numbers of turns Ns / Np, assuming an ideal transformer: Vs / Vp = Ns / Np.
变压器仅在交流电压下工作。它由绕在共同铁芯上的两个线圈组成。初级线圈中的交流电流产生变化的磁通，在次级线圈中感应出交变电动势。对于理想变压器，次级电压 Vs 与初级电压 Vp 之比等于匝数之比 Ns / Np：Vs / Vp = Ns / Np。
Vs / Vp = Ns / Np
Vs / Vp = Ns / Np（理想变压器）
Step‑up transformers increase voltage (Ns > Np) for high‑voltage transmission, reducing current and I²R losses in cables. Step‑down transformers then lower the voltage to safe levels for domestic use. Without the ability to transform a.c. voltages, the modern power grid would not be feasible. The transformer relationship also enables impedance matching in audio and radio circuits.
升压变压器（Ns > Np）提高电压，用于高压输电，降低电流和电缆中的 I²R 损耗。降压变压器随后将电压降至适合家用的安全水平。若无法对交流电压进行变压，现代电网将不可行。变压器的比例关系还能用于音频和无线电电路中的阻抗匹配。
10. Practical Applications and Safety Considerations | 实际应用与安全注意事项
Alternating voltages are ubiquitous: they power homes, offices and industry. Appliances are designed to operate at a specified rms voltage (e.g. 230 V in Europe). Many devices, such as laptop chargers, internally convert the mains a.c. to low‑voltage d.c. using rectifier‑smoother‑regulator circuits. Industrial motors often run on three‑phase a.c., which provides smoother power delivery.
交流电压无处不在：为家庭、办公室和工业供电。电器被设计在特定的均方根电压下工作（如欧洲的 230 V）。许多设备，如笔记本电脑充电器，使用整流‑滤波‑稳压电路将市电交流转换为低压直流。工业电机常采用三相交流电，以提供更平稳的动力输出。
Safety is paramount when dealing with alternating voltages. Even an rms voltage of 50 V can be lethal under certain conditions. Fuses and circuit breakers protect against overcurrent. Residual‑current devices (RCDs) detect leakage currents and rapidly cut the supply. Isolation transformers provide galvanic separation, protecting users from direct contact with mains live conductors. Always treat a.c. circuits with extreme caution.
处理交流电压时安全至关重要。在某些条件下，即使 50 V 的均方根电压也可能致命。熔断器和断路器用于过流保护。剩余电流装置（RCD）检测漏电流并迅速切断电源。隔离变压器提供电气隔离，保护用户不与市电火线直接接触。务必极其谨慎地对待交流电路。
Published by TutorHao | Physics Revision Series | aleveler.com
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