📚 Alternating Current | 交流电考点精讲
Alternating current (AC) is the backbone of modern electrical power systems. In A-Level Edexcel Physics, this topic covers the mathematical description of sinusoidal voltages and currents, the concept of root mean square (rms) values, power dissipation, transformers, and rectification. A solid understanding of AC not only prepares you for exams but also explains how electricity reaches our homes efficiently.
交流电是现代电力系统的支柱。在A-Level Edexcel物理中，该主题涵盖正弦电压和电流的数学描述、均方根值的概念、功率耗散、变压器以及整流。扎实掌握交流电不仅有助于备考，也能解释电力如何高效地输送到千家万户。
1. Sinusoidal Alternating Current and Voltage | 正弦交流电和电压
An alternating current or voltage changes direction and magnitude periodically. In mains electricity, the variation is sinusoidal. The instantaneous value of an AC voltage can be written as v = V0 sin(ωt), where V0 is the peak voltage, ω = 2πf is the angular frequency, and t is time. Similarly, the current is i = I0 sin(ωt) for a purely resistive circuit.
交流电或交流电压的幅值和方向周期性变化。在民用电力中，这种变化是正弦形式的。交流电压的瞬时值可表示为 v = V0 sin(ωt)，其中 V0 为峰值电压，ω = 2πf 为角频率，t 为时间。同理，对于纯电阻电路，电流为 i = I0 sin(ωt)。
The frequency f is 50 Hz in the UK, meaning the waveform completes 50 cycles per second. The period T = 1/f is 0.02 s. The sine function alternates between +V0 and –V0, giving the current its alternating nature.
英国电网频率 f 为 50 Hz，即波形每秒完成 50 个周期。周期 T = 1/f 为 0.02 s。正弦函数在 +V0 和 –V0 之间交替变化，使电流具有交变特性。
2. Peak, Peak-to-Peak, and Instantaneous Values | 峰值、峰峰值和瞬时值
The peak value V0 (or amplitude) is the maximum voltage reached during a cycle. The peak-to-peak voltage is 2V0, representing the total voltage swing. For UK mains, the rms voltage is 230 V, but the peak voltage is about 325 V because V0 = Vrms × √2.
峰值 V0（或振幅）是一个周期内达到的最大电压。峰峰电压为 2V0，代表电压的总摆动幅度。英国市电的均方根电压为 230 V，而峰值电压约为 325 V，因为 V0 = Vrms × √2。
The instantaneous voltage is the value at a specific time, obtained by substituting t into the sinusoidal equation. On an oscilloscope, you can read peak-to-peak values from the vertical scale and time period from the horizontal scale.
瞬时电压是某一特定时刻的值，通过将时间 t 代入正弦方程求得。在示波器上，可以从垂直刻度读出峰峰值，从水平刻度读周期。
3. Root Mean Square (RMS) Values | 均方根值
The root mean square (rms) value of an AC voltage or current is the equivalent DC value that would deliver the same average power to a resistor. For a sinusoidal waveform, Vrms = V0/√2 and Irms = I0/√2. These are the values typically quoted for mains electricity.
交流电压或电流的均方根值是一个等效的直流值，它能向电阻提供相同的平均功率。对于正弦波形，Vrms = V0/√2，Irms = I0/√2。这些通常是市电标称值。
The rms is calculated by squaring the instantaneous values, finding the mean of these squares over a full cycle, and then taking the square root. Because the square of a sine function averages to ½ over a complete cycle, we obtain the √2 factor.
均方根的计算步骤为：将瞬时值平方，求这些平方值在一个完整周期内的平均值，再开平方根。由于正弦函数的平方在一个完整周期内的平均值为 ½，因此得到了 √2 因子。
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For a sine wave: Vrms = V0/√2 ≈ 0.707 V0.
对于正弦波：Vrms = V0/√2 ≈ 0.707 V0。
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The rms value is always positive and used in power calculations: Pavg = IrmsVrms.
均方根值始终为正，并用于功率计算：Pavg = IrmsVrms。
4. Average Power in AC Circuits | 交流电路中的平均功率
In a purely resistive AC circuit, the power dissipated at any instant is p = vi = V0I0 sin²(ωt). Over a full cycle, the average value of sin²(ωt) is ½, so the average power is Pavg = ½ V0I0 = VrmsIrms. This is the same form as the DC power formula, which is why rms values are so useful.
在纯电阻交流电路中，任意时刻的耗散功率为 p = vi = V0I0 sin²(ωt)。在一个完整周期内，sin²(ωt) 的平均值为 ½，因此平均功率为 Pavg = ½ V0I0 = VrmsIrms。这与直流功率公式形式相同，因此均方根值如此有用。
It is important to note that the average power is not simply the product of average voltage and average current. The average voltage over a cycle is zero, but since power depends on the square of voltage or current, rms values must be used.
务必注意：平均功率并非平均电压与平均电流的简单乘积。一个周期内的平均电压为零，但由于功率取决于电压或电流的平方，必须使用均方根值。
5. AC in Resistors | 交流电路中的电阻
When an alternating voltage is applied to a pure resistor, the current and voltage are in phase. The resistance R follows Ohm’s Law for instantaneous, peak, and rms values: V = IR, V0 = I0R, and Vrms = IrmsR. There is no phase difference between v and i, and the power factor is 1.
当交流电压施加于纯电阻时，电流与电压同相。电阻 R 对于瞬时值、峰值和均方根值均遵循欧姆定律：V = IR，V0 = I0R，Vrms = IrmsR。v 与 i 之间没有相位差，功率因数为 1。
A common experiment uses a signal generator, a resistor, and an oscilloscope to show that the current waveform exactly mirrors the voltage waveform. This confirms the linear behaviour of resistors in AC circuits.
常见的实验是用信号发生器、电阻和示波器来展示电流波形与电压波形完全一致，这验证了电阻在交流电路中的线性行为。
6. Ideal Transformer Principles | 理想变压器原理
A transformer changes the voltage level of an AC supply using electromagnetic induction. It consists of two coils wound on a common soft-iron core. An alternating current in the primary coil produces a changing magnetic flux, which links the secondary coil and induces an alternating emf.
变压器利用电磁感应改变交流电源的电压水平。它由绕在共用软铁芯上的两个线圈组成。初级线圈中的交流电产生变化的磁通量，该磁通量交链次级线圈并感应出交变电动势。
In an ideal transformer with no energy losses, the flux linkage per turn is the same for both coils. Thus, the induced emf per turn is equal. This leads to the turns–voltage relationship: Vp/Vs = Np/Ns, where Np and Ns are the numbers of turns on the primary and secondary.
在无能量损耗的理想变压器中，每匝的磁链相同。因此，每匝感应电动势相等。由此得出匝比–电压关系：Vp/Vs = Np/Ns，其中 Np 和 Ns 分别为初级和次级的匝数。
7. Transformer Equation and Efficiency | 变压器方程与效率
For an ideal transformer, input power equals output power: IpVp = IsVs. Combining with the turns ratio gives Ip/Is = Vs/Vp = Ns/Np. This shows that a step–down transformer reduces voltage but increases current, and a step–up transformer does the opposite.
对于理想变压器，输入功率等于输出功率：IpVp = IsVs。结合匝比关系可得 Ip/Is = Vs/Vp = Ns/Np。这说明降压变压器降低电压但增大电流，升压变压器则相反。
Real transformers have losses due to eddy currents, hysteresis, and resistance in the windings. Efficiency η = (output power / input power) × 100%. Laminated cores and low-resistance copper wire are used to minimise losses, and typical efficiencies exceed 99% for large transformers.
实际变压器因涡流、磁滞和线圈电阻而产生损耗。效率 η =（输出功率/输入功率）× 100%。使用叠片铁心和低电阻铜线可以减小损耗，大型变压器的典型效率超过 99%。
The key transformer equations are:
Vp/Vs = Np/Ns
Ip/Is = Ns/Np
关键变压器方程为：匝比–电压比和电流比关系。
8. Half-Wave and Full-Wave Rectification | 半波和全波整流
Rectification converts AC to DC. A single diode produces half-wave rectification, where only one half of each AC cycle is allowed through. The output is a series of positive pulses, with a large ripple and a non-zero average voltage equal to V0/π.
整流将交流电转换为直流电。单个二极管实现半波整流，只允许交流电的半个周期通过。输出是一系列正脉冲，纹波很大，平均电压为 V0/π。
In full-wave rectification using four diodes in a bridge arrangement, both halves of the AC cycle are used. The negative half is flipped to become positive, giving a smoother output with an average voltage of 2V0/π. This is the basis of most DC power supplies.
全波整流使用四个二极管组成的桥式电路，交流电的两个半周都被利用。负半周被翻转为正，输出更平滑，平均电压为 2V0/π。这是大多数直流电源的基础。
9. Smoothing and Ripple | 平滑滤波和纹波
A capacitor placed across the rectifier output smooths the voltage by charging during the peak and discharging through the load when the rectified voltage drops. This reduces the ripple, the small residual variation in the DC voltage.
在整流输出端并联一个电容，通过在峰值时充电并在整流电压下降时通过负载放电来平滑电压。这减小了纹波，即直流电压中残留的小幅波动。
The amount of ripple depends on the capacitance C and the load resistance R. A larger time constant RC reduces the ripple, but a very large capacitor can cause a high initial surge current. The smoothed output is approximately DC with a slight sawtooth waveform.
纹波的大小取决于电容 C 和负载电阻 R。较大的时间常数 RC 可减小纹波，但过大的电容会引起较高的初始浪涌电流。平滑后的输出接近直流，带有轻微的锯齿波形。
10. Applications of AC and Transformers | 交流电和变压器的应用
AC is used for power transmission because its voltage can easily be stepped up or down with transformers. High-voltage transmission reduces current for a given power, minimising I²R losses in cables. The National Grid uses typical transmission voltages of 400 kV or 275 kV, stepped down to 230 V for domestic use.
交流电用于电力传输，因为它的电压可通过变压器轻松升降。对于给定功率，高压输电可降低电流，从而减小电缆中的 I²R 损耗。国家电网使用的典型输电电压为 400 kV 或 275 kV，经降压至 230 V 供家庭使用。
Transformers also appear in phone chargers, laptop adapters, and isolation transformers for safety. Step-down transformers reduce voltage to safe levels for electronic circuits, while step-up transformers are essential in X-ray machines and microwave ovens.
变压器也出现在手机充电器、笔记本电脑适配器和安全隔离变压器中。降压变压器将电压降低到电子电路所需的安全水平，而升压变压器在 X 射线机和微波炉中必不可少。
11. Measuring AC and Oscilloscopes | 交流电测量和示波器
An oscilloscope displays a waveform of voltage against time. For AC measurements, you can determine the peak voltage V0 from the vertical sensitivity (volts/div) and the number of vertical divisions. The period T is found from the timebase setting (time/div) and horizontal divisions, giving f = 1/T.
示波器显示电压随时间变化的波形。对于交流电测量，可从垂直灵敏度（伏/格）和垂直格数确定峰值电压 V0。根据时基设置（时间/格）和水平格数求出周期 T，从而得到 f = 1/T。
A digital multimeter set to AC mode displays the rms value, assuming a sinusoidal input. Some meters are ‘true rms’ and can measure non-sinusoidal waveforms accurately. Always check whether the instrument reads peak, peak-to-peak, or rms.
设置到交流模式的数字万用表显示均方根值，并假定输入为正弦波。某些仪表为“真有效值”型，能准确测量非正弦波形。务必核实仪器读数是峰值、峰峰值还是均方根值。
12. Key Formulas Summary | 关键公式汇总
Memorising these relationships is essential for the exam:
记住以下关系对考试至关重要：
| Formula | Description |
|---|---|
| v = V0 sin(ωt) | Instantaneous voltage |
| i = I0 sin(ωt) | Instantaneous current |
| Vrms = V0/√2 | RMS voltage |
| Irms = I0/√2 | RMS current |
| Pavg = VrmsIrms | Average power |
| Vp/Vs = Np/Ns | Transformer voltage ratio |
| Ip/Is = Ns/Np | Transformer current ratio |
| η = (Pout/Pin) × 100% | Efficiency |
| f = 1/T | Frequency |
Understanding these formulas and their derivations, along with the practical aspects of AC circuits, will give you confidence in tackling any A-Level Edexcel Physics question on alternating currents.
理解这些公式及其推导，结合交流电路的实践应用，将使你在应对任何A-Level Edexcel物理交流电题目时充满信心。
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