Alternating Voltages | 交流电压

📚 Alternating Voltages | 交流电压

Alternating voltages are central to mains electricity and to many topics in CIE A Level Physics. Understanding how they vary with time, how to measure them, and how they are transformed or rectified is essential for both examinations and practical applications.

交流电压是市电以及 CIE A Level 物理许多专题的核心。理解它如何随时间变化、如何测量、如何变压或整流，对考试和实际应用都至关重要。

1. What is an Alternating Voltage? | 什么是交流电压

An alternating voltage is a potential difference that reverses its polarity in a regular, repeating way. Unlike a direct voltage from a battery, which keeps one terminal positive and the other negative, an alternating voltage drives the current first in one direction and then in the opposite direction. The most common alternating voltage has a sinusoidal waveform, so its instantaneous value changes smoothly between positive and negative peaks. Mains electricity is a familiar example: in the UK it alternates with a frequency of 50 Hz.

交流电压是一种极性按规律周期性反转的电势差。与电池提供的直流电压不同——电池始终让一个端子为正、另一个为负——交流电压驱动电流先朝一个方向流动，再朝相反方向流动。最常见的交流电压具有正弦波形，因此其瞬时值在正峰值和负峰值之间平滑变化。市电就是一个熟悉的例子：在英国，它以 50 Hz 的频率交替变化。

2. Sinusoidal Waveform and Key Terms | 正弦波形与关键术语

For a sinusoidal alternating voltage, the instantaneous voltage v can be described by v = V₀ sin(2πft) or v = V₀ sin(ωt), where V₀ is the peak voltage, f is the frequency and ω is the angular frequency. The waveform rises from zero to +V₀, falls back through zero to −V₀, and then returns to zero in one complete cycle. Key terms used to describe this waveform include peak value, period, frequency and phase. The sine function ensures the voltage changes most rapidly at zero crossing and most slowly near the peaks.

对于正弦交流电压，瞬时电压 v 可以写成 v = V₀ sin(2πft) 或 v = V₀ sin(ωt)，其中 V₀ 是峰值电压，f 是频率，ω 是角频率。波形在一个完整周期内从零上升到 +V₀，再回落到零并继续到 −V₀，最后回到零。描述这一波形时常用的关键术语包括峰值、周期、频率和相位。正弦函数使得电压在过零点变化最快，而在峰值附近变化最慢。

v = V₀ sin(2πft) = V₀ sin(ωt)

3. Frequency, Period and Angular Frequency | 频率、周期与角频率

The period T is the time taken for one complete cycle of the alternating voltage. Frequency f is the number of cycles per second, so f = 1/T. Angular frequency ω is related to frequency by ω = 2πf and has units of radians per second. For a 50 Hz mains supply, the period is T = 1/50 = 0.020 s or 20 ms. In a 60 Hz system, the period is about 16.7 ms. These three quantities allow the waveform equation to be written in alternative but equivalent forms.

周期 T 是交流电压完成一个完整循环所需的时间。频率 f 是每秒钟的循环数，因此 f = 1/T。角频率 ω 与频率的关系为 ω = 2πf，单位为弧度每秒。对于 50 Hz 的市电，周期为 T = 1/50 = 0.020 s，即 20 ms。在 60 Hz 系统中，周期约为 16.7 ms。这三个量使得波形方程可以写成不同但等价的形式。

f = 1/T, ω = 2πf

4. Peak, Peak-to-Peak and Instantaneous Values | 峰值、峰峰值与瞬时值

The peak value V₀ is the maximum voltage reached in either the positive or negative direction. The peak-to-peak voltage V_pp is the full vertical range from +V₀ to −V₀, so V_pp = 2V₀. The instantaneous value v(t) is the voltage at a particular time and can be found by substituting t into v = V₀ sin(2πft). When using an oscilloscope, it is often easiest to measure V_pp and then divide by two to obtain V₀. For example, if V_pp is 6.0 V, the peak voltage V₀ is 3.0 V.

峰值 V₀ 是电压在正方向或负方向达到的最大值。峰峰值 V_pp 是从 +V₀ 到 −V₀ 的完整垂直范围，因此 V_pp = 2V₀。瞬时值 v(t) 是某一特定时刻的电压，可将 t 代入 v = V₀ sin

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