📚 A2 Physics: Alternating Current Mastery Guide | A2 物理：交流电 考点精讲
Alternating current (AC) is fundamental to modern electrical power systems and appears extensively in A2 Physics exams. Mastering its theory, from sinusoidal generation to transformer efficiency and LCR resonance, is vital for high marks. This guide breaks down every essential concept with concise English explanations and matching Chinese translations, ensuring bilingual clarity.
交流电是现代电力系统的基础，也是 A2 物理考试的重中之重。从正弦波产生到变压器效率，再到 LCR 谐振，掌握这些理论对于拿到高分至关重要。本文以精要的英文讲解搭配对应中文译文，逐点突破，助你双语通透。
1. What is Alternating Current? | 什么是交流电？
An alternating current is an electric current that periodically reverses direction and varies in magnitude continuously with time, typically following a sinusoidal function.
交流电是一种周期性地改变方向并随时间连续变化大小的电流，通常按正弦函数规律变化。
The alternating potential difference (voltage) supplied by mains electricity in most countries has a frequency of 50 Hz or 60 Hz, meaning it completes 50 or 60 full cycles per second.
大多数国家市电提供的交流电压频率为 50 Hz 或 60 Hz，即每秒完成 50 或 60 个完整周期。
In contrast, direct current (DC) flows in only one direction with a constant magnitude, as from a battery.
相比之下，直流电 (DC) 仅沿一个方向流动且大小恒定，例如电池提供的电流。
2. Sinusoidal Waveform & Key Values | 正弦波形与关键值
The instantaneous voltage of an AC supply can be described by the equation:
交流电源的瞬时电压可由下式描述：
v = V₀ sin(ωt)
Here, V₀ is the peak voltage, ω is the angular frequency (ω = 2πf), and t is time. The current follows i = I₀ sin(ωt) for a purely resistive load.
式中 V₀ 为峰值电压，ω 为角频率 (ω = 2πf)，t 为时间。对于纯电阻负载，电流遵循 i = I₀ sin(ωt)。
The peak-to-peak voltage Vₚₚ is the difference between maximum positive and maximum negative values, equal to 2V₀. The period T = 1/f, and the frequency f is the number of cycles per second.
峰峰值电压 Vₚₚ 是最大正值与最大负值之差，等于 2V₀。周期 T = 1/f，频率 f 为每秒的周期数。
Key values on the waveform are essential for calculating average power and understanding rectification.
波形上的这些关键值对于计算平均功率和理解整流过程至关重要。
3. RMS Values: Root Mean Square | 均方根值 (RMS)
Since AC varies continuously, we use the root mean square (RMS) value to equate it to an equivalent DC that would deliver the same heating effect in a resistor.
由于交流电持续变化，我们使用均方根值 (RMS) 将其等效为在电阻上产生相同热效应的直流电。
For a sinusoidal waveform, the RMS voltage and current are:
对于正弦波形，RMS 电压和电流为：
Vᵣₘₛ = V₀ / √2 Iᵣₘₛ = I₀ / √2
Mains electricity in the UK is rated at 230 V; this is the RMS value. The peak voltage is therefore about 325 V.
英国市电标称 230 V，这是 RMS 值，因此峰值电压约为 325 V。
RMS values are used to compute average power: Pavg = Iᵣₘₛ Vᵣₘₛ for a purely resistive circuit.
RMS 值用于计算平均功率：对于纯电阻电路，Pavg = Iᵣₘₛ Vᵣₘₛ。
All AC voltmeters and ammeters (except peak-reading types) display RMS values unless stated otherwise.
除非另有说明，所有交流电压表和电流表（峰值读数型除外）显示的都是 RMS 值。
4. AC Generators (Alternators) | 交流发电机
A simple AC generator consists of a coil rotating in a uniform magnetic field. As the coil turns, the magnetic flux linkage changes, inducing an alternating EMF according to Faraday’s law.
简单的交流发电机由一个在匀强磁场中旋转的线圈构成。线圈转动时，磁通链发生变化，根据法拉第定律感应出交变电动势。
The induced EMF at any instant is given by:
任意时刻的感应电动势为：
ε = NB A ω sin(ωt) = ε₀ sin(ωt)
where N is the number of turns, B the magnetic flux density, A the coil area, and ω the angular speed.
其中 N 为线圈匝数，B 为磁通密度，A 为线圈面积，ω 为角速度。
Slip rings and carbon brushes allow the alternating output to be taken from the rotating coil without tangling the wires.
滑环和碳刷使得能从旋转线圈中引出交变输出而不使导线缠绕。
The frequency of the generated AC equals the rotational frequency of the coil, f = ω/2π.
产生的交流电频率等于线圈的旋转频率，即 f = ω/2π。
5. Transformers: Principles & Efficiency | 变压器：原理与效率
A transformer uses electromagnetic induction to change the voltage of an AC supply. It consists of two coils wound on a soft iron core. An alternating current in the primary coil creates a changing magnetic flux, which links the secondary coil and induces an EMF.
变压器利用电磁感应改变交流电压。它由绕在软铁芯上的两个线圈组成。初级线圈中的交流电产生变化磁通，该磁通链接次级线圈并感应出电动势。
For an ideal transformer with no energy losses, the voltage and turns ratios are equal:
对于无能量损耗的理想变压器，电压比等于匝数比：
Vₚ / Vₛ = Nₚ / Nₛ
and, with power in = power out, IₚVₚ = IₛVₛ.
且因输入功率等于输出功率，IₚVₚ = IₛVₛ。
Real transformers experience losses from resistance heating (copper loss), eddy currents, and hysteresis in the core. Efficiency is given by η = (output power / input power) × 100%.
实际变压器存在电阻发热（铜损）、涡流和磁滞等损耗。效率 η = (输出功率 / 输入功率) × 100%。
To reduce eddy currents, the core is laminated; to minimise hysteresis, a soft magnetic material is used.
为减少涡流，铁芯采用叠片结构；为降低磁滞，使用软磁性材料。
6. Half-Wave and Full-Wave Rectification | 半波整流与全波整流
Rectification converts AC into DC using diodes, which allow current to flow in only one direction.
整流利用单向导电的二极管将交流电转换为直流电。
Half-wave rectification uses a single diode. It passes only the positive (or negative) half of each AC cycle, resulting in a pulsating DC with large gaps.
半波整流使用单个二极管，仅通过交流周期的一半（正半周或负半周），产生带有大间隔的脉动直流。
Full-wave rectification uses a bridge rectifier (four diodes) or a centre-tapped transformer with two diodes. It inverts the negative half-cycles into positive ones, giving a much smoother output with a higher mean voltage.
全波整流使用桥式整流器（四个二极管）或带中心抽头的变压器与两个二极管。它将负半周翻转为正半周，输出更平滑，平均电压更高。
The table below compares the two types:
下表对两种整流方式进行了比较：
| Feature | Half-wave | Full-wave |
|---|---|---|
| Number of diodes | 1 | 4 (bridge) or 2 (centre-tap) |
| Output frequency | Same as input | Double the input |
| Average DC voltage | V₀/π ≈ 0.318V₀ | 2V₀/π ≈ 0.637V₀ |
| Ripple | Large gaps | Smaller gaps, easier to smooth |
7. Smoothing and Ripple | 滤波与纹波
After rectification, the DC output still fluctuates. A capacitor connected in parallel with the load acts as a reservoir, charging when the voltage rises and discharging when it falls, thus smoothing the waveform.
整流后的直流输出仍有波动。与负载并联的电容器起到储能作用，电压上升时充电、下降时放电，从而平滑波形。
The remaining variation is called ripple. For full-wave rectification, the approximate peak-to-peak ripple voltage is:
剩余的波动称为纹波。对于全波整流，近似的峰峰值纹波电压为：
Vripple ≈ Iload / (f × C)
where Iload is the load current, f the ripple frequency (twice mains frequency for full-wave), and C the capacitance. Larger C or smaller load current reduces ripple.
其中 Iload 为负载电流，f 为纹波频率（全波整流时为市电频率的两倍），C 为电容值。增大电容或减小负载电流可减小纹波。
A voltage regulator may be added after the capacitor to provide a steady DC output regardless of load variations.
可在电容之后加入稳压器，以便在负载变化时提供稳定的直流输出。
8. Reactance: Capacitive & Inductive | 容抗与感抗
In AC circuits, capacitors and inductors oppose current flow not by resistance but by reactance, which depends on frequency.
在交流电路中，电容器和电感器不是通过电阻而是通过电抗来阻碍电流，电抗取决于频率。
Capacitive reactance Xc is given by:
容抗 Xc 由下式给出：
Xc = 1 / (2πfC) = 1 / (ωC)
It decreases as frequency increases. In a purely capacitive circuit, the current leads the voltage by 90° (φ = –π/2).
容抗随频率升高而减小。在纯电容电路中，电流超前电压 90° (φ = –π/2)。
Inductive reactance Xₗ is given by:
感抗 Xₗ 为：
Xₗ = 2πfL = ωL
It increases with frequency. In a purely inductive circuit, the current lags the voltage by 90° (φ = +π/2).
感抗随频率升高而增大。在纯电感电路中，电流滞后电压 90° (φ = +π/2)。
These phase differences are crucial when analysing combined circuits using phasors.
这些相位差在用相量分析组合电路时至关重要。
9. Impedance and Phasor Diagrams | 阻抗与相量图
Impedance Z is the total opposition to AC in a circuit containing resistance, inductance, and capacitance. It combines resistance and reactance as a vector sum.
阻抗 Z 是包含电阻、电感和电容的电路中对交流的总阻碍，它是电阻与电抗的矢量和。
For a series LCR circuit, the magnitude of impedance is:
对于串联 LCR 电路，阻抗的大小为：
Z = √(R² + (Xₗ – Xc)²)
The phase angle φ between the supply voltage and current is given by tan φ = (Xₗ – Xc) / R.
电源电压与电流之间的相位角 φ 由 tan φ = (Xₗ – Xc) / R 给出。
Phasor diagrams represent the voltages across each component as rotating vectors. The supply voltage is the vector sum of V_R, Vₗ, and Vc. At resonance, Vₗ and Vc cancel, leaving V = V_R.
相量图将各元件上的电压表示为旋转矢量。电源电压是 V_R、Vₗ 和 Vc 的矢量和。谐振时 Vₗ 与 Vc 抵消，得到 V = V_R。
Impedance determines the current amplitude: I₀ = V₀ / Z.
阻抗决定电流幅值：I₀ = V₀ / Z。
10. Series LCR Circuit & Resonance | 串联 LCR 电路与谐振
A series LCR circuit exhibits a special condition called resonance when the inductive and capacitive reactances are equal: Xₗ = Xc.
当感抗与容抗相等 (Xₗ = Xc) 时，串联 LCR 电路出现一种特殊状态，称为谐振。
The resonant angular frequency ω₀ and the corresponding linear frequency f₀ are:
谐振角频率 ω₀ 及相应的线性频率 f₀ 为：
ω₀ = 1 / √(LC) f₀ = 1 / (2π√(LC))
At resonance, impedance is minimum and equals the resistance R, so the current is maximum (I₀ = V₀ / R). The circuit behaves as if it were purely resistive, with φ = 0.
谐振时阻抗最小且等于电阻 R，因此电流最大 (I₀ = V₀ / R)。电路表现为纯电阻性，φ = 0。
The sharpness of resonance is described by the quality factor Q. A high Q circuit has low resistance and a very sharp current peak, useful for tuning radio receivers.
谐振的尖锐程度用品质因数 Q 描述。高 Q 电路电阻低、电流峰非常尖锐，适用于无线电接收机调谐。
At resonance, the voltage across the inductor or capacitor can be many times larger than the supply voltage (Vₗ = Q × Vsupply).
谐振时，电感或电容两端的电压可能比电源电压大很多倍 (Vₗ = Q × Vsupply)。
11. Power in AC Circuits & Power Factor | 交流电路中的功率与功率因数
In AC circuits, the instantaneous power p = vi varies with time. The average power absorbed by a circuit over a complete cycle is:
在交流电路中，瞬时功率 p = vi 随时间变化。一个完整周期内电路吸收的平均功率为：
Pavg = Vᵣₘₛ Iᵣₘₛ cos φ
where cos φ is the power factor. It indicates the fraction of the volt-amp product that does useful work.
式中 cos φ 为功率因数，表示伏安乘积中实际做功的份数。
For a purely resistive load, φ = 0, cos φ = 1, and all power is dissipated. For purely reactive loads, φ = ±90°, cos φ = 0, and average power is zero – energy oscillates between source and reactance.
纯电阻负载下 φ = 0、cos φ = 1，功率全被消耗；纯电抗负载下 φ = ±90°、cos φ = 0，平均功率为零——能量在电源与电抗间振荡。
The apparent power S = Vᵣₘₛ Iᵣₘₛ (in VA), while the real power P = S cos φ (in W). The reactive power Q = S sin φ (in VAR).
视在功率 S = Vᵣₘₛ Iᵣₘₛ (单位 VA)，有功功率 P = S cos φ (单位 W)，无功功率 Q = S sin φ (单位 VAR)。
A low power factor means larger current is needed for the same real power, increasing transmission losses. Industrial users often improve power factor using capacitor banks.
低功率因数意味着传递相同有功功率需要更大电流，增加传输损耗。工业用户常通过电容器组改善功率因数。
Published by TutorHao | Physics Revision Series | aleveler.com
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