📚 IB Physics: Alternating Current Key Revision Points | IB 物理：交流电考点精讲
Alternating current (AC) is central to the IB Physics syllabus, linking electromagnetic induction, circuit theory, and real‑world power systems. A thorough grasp of AC concepts—from rms values to transformer principles—is essential for both HL and SL candidates, especially when tackling Paper 2 and Paper 3 questions on electricity and magnetism.
交流电是 IB 物理大纲的核心内容，它将电磁感应、电路理论与实际电力系统联系在一起。无论 HL 还是 SL，透彻掌握交流电的概念——从均方根值到变压器原理——都是应对 Paper 2 和 Paper 3 中电学与磁学考题的关键。
1. Introduction to Alternating Current | 交流电概述
An alternating current is an electric current whose magnitude and direction vary cyclically, typically in a sinusoidal waveform. In contrast, direct current (DC) flows steadily in a single direction.
交流电是大小和方向呈周期性变化的电流，通常呈正弦波形。与之相对，直流电（DC）则是单向稳定流动的电流。
The instantaneous value of an AC voltage is often expressed as v = V₀ sin(ωt), where V₀ is the peak voltage, ω the angular frequency, and t time.
交流电压的瞬时值常表示为 v = V₀ sin(ωt)，其中 V₀ 为峰值电压，ω 为角频率，t 为时间。
Angular frequency ω is related to ordinary frequency f and period T by ω = 2πf = 2π/T.
角频率 ω 与普通频率 f 及周期 T 的关系为 ω = 2πf = 2π/T。
Mains electricity in many countries has a frequency of 50 Hz, meaning ω = 100π rad s⁻¹, while in others it is 60 Hz.
许多国家的市电频率为 50 Hz，即 ω = 100π rad s⁻¹；而在另一些国家则为 60 Hz。
2. Generating an AC Voltage | 交流电压的产生
A basic AC generator (alternator) consists of a coil rotating in a uniform magnetic field. The induced emf, according to Faraday’s law, is ε = NBAω sin(ωt), producing a sinusoidal output.
简单的交流发电机（交流发电机）由在均匀磁场中旋转的线圈构成。根据法拉第定律，其感应电动势为 ε = NBAω sin(ωt)，输出为正弦波形。
The peak emf ε₀ occurs when the plane of the coil is parallel to the magnetic field, so ε₀ = NBAω, where N is the number of turns, B the magnetic flux density, and A the coil area.
峰值电动势 ε₀ 出现在线圈平面与磁场平行时，因此 ε₀ = NBAω，其中 N 为线圈匝数，B 为磁通密度，A 为线圈面积。
Slip rings and brushes maintain electrical contact without twisting the wires, allowing the alternating emf to be supplied to an external circuit.
滑环和电刷可在不绞线的情况下保持电接触，从而将交变电动势输出至外电路。
3. Peak, Peak‑to‑Peak and RMS Values | 峰值、峰峰值与有效值
The peak value (V₀ or I₀) is the maximum magnitude reached in each cycle. The peak‑to‑peak value is twice the peak value, spanning from the positive to the negative maximum.
峰值（V₀ 或 I₀）是每个周期内达到的最大值。峰峰值为峰值的两倍，即从正最大值到负最大值之间的跨度。
Since AC varies, we often use the root‑mean‑square (rms) value to represent the equivalent DC heating effect. For sinusoidal waveforms: Vrms = V₀/√2 and Irms = I₀/√2.
由于交流电持续变化，我们常使用均方根（rms）值来表示其等效的直流热效应。对于正弦波形：Vrms = V₀/√2，Irms = I₀/√2。
In the IB data booklet, the relationship is given as Irms = I₀/√2. Remember, this factor applies only to sinusoidal AC.
在 IB 数据手册中，该关系式表示为 Irms = I₀/√2。请记住，这一系数仅适用于正弦交流电。
Mains voltage quoted as 230 V in Europe is an rms value; the corresponding peak voltage is 230√2 ≈ 325 V.
欧洲市电标称 230 V 是有效值；相应的峰值电压为 230√2 ≈ 325 V。
4. Power in AC Circuits | 交流电路中的功率
The instantaneous power is p = vi, but the quantity of practical interest is average power. For a purely resistive load, average power is Pavg = IrmsVrms = ½ I₀ V₀.
瞬时功率为 p = vi，但有实际意义的是平均功率。对于纯电阻负载，平均功率为 Pavg = IrmsVrms = ½ I₀ V₀。
When reactance causes a phase difference φ between current and voltage, the average power becomes Pavg = IrmsVrms cos φ, where cos φ is the power factor.
当电抗导致电流与电压之间存在相位差 φ 时，平均功率变为 Pavg = IrmsVrms cos φ，其中 cos φ 为功率因数。
A power factor of 1 means that current and voltage are in phase, delivering maximum working power. A lower power factor means more current flows for the same useful power, causing larger I²R losses in transmission.
功率因数为 1 表示电流与电压同相，提供最大有功功率。较低的功率因数意味着为传输同样大小的有用功率需要更大的电流，从而在输电过程中产生更大的 I²R 损耗。
5. Resistance, Reactance and Impedance | 电阻、电抗与阻抗
In DC circuits, opposition to current is called resistance (R). In AC circuits, capacitors and inductors introduce an additional opposition known as reactance (X), which depends on frequency.
在直流电路中，对电流的阻碍称为电阻（R）。在交流电路中，电容器和电感器还会引入一种与频率相关的额外阻碍，称为电抗（X）。
The total opposition in an AC circuit is impedance (Z), measured in ohms. For a series LCR circuit, impedance is given by Z = √(R² + (XL − XC)²).
交流电路中的总阻碍称为阻抗（Z），单位为欧姆。对于串联 LCR 电路，阻抗由 Z = √(R² + (XL − XC)²) 给出。
Only the resistive part of impedance dissipates energy; pure reactance stores and returns energy to the circuit without net power loss.
只有阻抗中的电阻部分耗散能量；纯电抗仅储存能量并返还至电路，没有净功率损耗。
6. Capacitive and Inductive Reactance | 容抗与感抗
Inductive reactance arises from the back emf induced in a coil as current changes. Its magnitude is XL = ωL = 2πf L, so it increases linearly with frequency.
感抗源于电流变化时线圈中感应出的反电动势。其大小为 XL = ωL = 2πf L，因此随频率线性增加。
Capacitive reactance is due to the charging and discharging of a capacitor. It is given by XC = 1/(ωC) = 1/(2πf C), decreasing as frequency rises.
容抗来自电容器的充放电过程。它由 XC = 1/(ωC) = 1/(2πf C) 给出，随频率升高而减小。
At very high frequencies, an inductor behaves almost as an open circuit, while a capacitor acts nearly as a short circuit; at DC, the inductor is a short and the capacitor is an open circuit.
在极高频率下，电感几乎相当于开路，而电容几乎相当于短路；在直流情况下，电感相当于短路，电容相当于开路。
7. Phase Relationships | 相位关系
In a purely resistive AC circuit, the current and voltage are in phase: both reach zero and peak simultaneously.
在纯电阻交流电路中，电流与电压同相：二者同时达到零值和峰值。
In a purely inductive circuit, the voltage leads the current by 90° (π/2 rad), or equivalently, the current lags the voltage by 90°.
在纯电感电路中，电压超前电流 90°（π/2 rad），或者说电流滞后电压 90°。
In a purely capacitive circuit, the current leads the voltage by 90°, meaning the voltage lags the current by 90°. The mnemonics ‘ELI the ICE man’ are useful: for inductor (L), E (voltage) leads I (current); for capacitor (C), I leads E.
在纯电容电路中，电流超前电压 90°，即电压滞后电流 90°。记忆口诀“ELI the ICE man”很有用：电感 (L) 时，E（电压）领先 I（电流）；电容 (C) 时，I 领先 E。
In a series LCR circuit, the phase angle φ between the total voltage and current satisfies tan φ = (XL − XC) / R. If XL > XC, the circuit is inductive (voltage leads); if XC > XL, it is capacitive (current leads).
在串联 LCR 电路中，总电压与电流之间的相位角 φ 满足 tan φ = (XL − XC) / R。若 XL > XC 则电路呈感性（电压超前）；若 XC > XL 则呈容性（电流超前）。
8. Phasor Diagrams | 相量图
A phasor is a rotating vector that represents a sinusoidally varying quantity. Its length equals the peak value, and its angle with the horizontal axis indicates its phase.
相量是表示正弦变化量的旋转矢量。其长度等于峰值，与水平轴的夹角表示相位。
In an LCR circuit, the resistor voltage phasor VR is drawn along the reference axis. The inductor phasor VL is drawn 90° ahead, and the capacitor phasor VC is drawn 90° behind the current phasor.
在 LCR 电路中，电阻电压相量 VR 沿参考轴画出；电感相量 VL 画在超前 90° 方向；电容相量 VC 画在滞后电流相量 90° 的方向。
The supply voltage phasor V is the vector sum of VR, VL and VC, forming a right‑angled triangle with hypotenuse ZI. This leads directly to the impedance triangle and the power factor cos φ = R/Z.
电源电压相量 V 是 VR、VL 和 VC 的矢量和，形成一个以 ZI 为斜边的直角三角形。由此可直接得出阻抗三角形及功率因数 cos φ = R/Z。
Phasor diagrams are invaluable for solving problems involving multi‑element AC circuits without having to manipulate trigonometric equations directly.
相量图对于求解含多元件交流电路的问题极有价值，可免去直接处理三角方程式的繁琐。
9. Series LCR Circuit and Resonance | 串联 LCR 电路与共振
A series LCR circuit exhibits resonance when the inductive and capacitive reactances are equal: XL = XC. This gives the resonance frequency f₀ = 1/(2π√(LC)).
串联 LCR 电路在感抗与容抗相等时发生共振：XL = XC。此时的共振频率为 f₀ = 1/(2π√(LC))。
At resonance, the impedance is purely resistive and at a minimum (Z = R), so the current reaches its maximum value Imax = V/R. The phase angle φ = 0, giving a power factor of 1.
共振时，阻抗呈纯电阻性且为最小值（Z = R），因此电流达到最大值 Imax = V/R。相位角 φ = 0，功率因数为 1。
The sharpness of resonance is described by the quality factor Q. A high‑Q circuit has a narrow, sharply peaked response and is very frequency‑selective, which is exploited in radio tuning.
共振的尖锐程度由品质因数 Q 描述。高 Q 值电路具有窄而尖锐的响应峰，频率选择性很强，广泛应用于无线电调谐。
Voltage magnification occurs at resonance: the voltage across L or C can be many times greater than the supply voltage (VL = VC = Q × V), which can be dangerous in high‑power systems.
共振时会出现电压放大现象：电感或电容两端的电压可能远大于电源电压（VL = VC = Q × V），在高压系统中这可能是危险的。
10. The Transformer | 变压器
An ideal transformer works on the principle of mutual induction, changing the voltage and current levels while keeping power approximately constant (VpIp ≈ VsIs).
理想变压器基于互感应原理工作，改变电压与电流水平，同时使功率近似保持不变（VpIp ≈ VsIs）。
The turn ratio determines the transformation: Vs/Vp = Ns/Np and Ip/Is = Ns/Np. A step‑up transformer has Ns > Np, raising voltage and reducing current.
匝数比决定变换关系：Vs/Vp = Ns/Np 且 Ip/Is = Ns/Np。升压变压器 Ns > Np，可升高电压、减小电流。
Energy losses in real transformers come from resistive heating in the coils (copper loss), eddy currents in the core, and hysteresis. Laminated soft‑iron cores reduce eddy currents.
实际变压器中的能量损耗来自线圈电阻发热（铜损）、铁芯中的涡流以及磁滞。使用叠片软铁芯可减小涡流。
IB frequently explores the efficiency of a transformer, often asking you to calculate input/output power and identify why it is less than 100%.
IB 考试常探究变压器效率问题，往往会要求计算输入/输出功率，并说明效率为何低于 100%。
11. Power Transmission and High Voltage | 电力传输与高电压
Electrical energy is transmitted at high voltages (e.g., 132 kV, 400 kV) to minimise I²R power loss in the cables. Since P = IV, for a given power, a higher voltage means a lower current.
电能以高压（如 132 kV、400 kV）传输，以最大限度减少电缆中的 I²R 功率损耗。由于 P = IV，对于给定功率，电压越高则电流越小。
The power lost in transmission lines is Ploss = I²R, where R is the total resistance of the wires. Halving the current reduces the loss by a factor of 4.
输电线路中损耗的功率为 Ploss = I²R，其中 R 为导线总电阻。电流减半可使损耗降至原来的四分之一。
A typical grid system uses step‑up transformers at the power station and step‑down transformers near consumers, ensuring safe, efficient distribution.
典型的电网系统在发电站使用升压变压器，在用户附近使用降压变压器，从而确保安全高效的配电。
IB questions may connect transmission loss calculations to the concepts of rms current, resistance per unit length, and the environmental benefits of reduced energy waste.
IB 试题常常将输电损耗计算与有效值电流、单位长度电阻以及减少能源浪费对环境的益处等概念相结合。
12. Rectification: AC to DC Conversion | 整流：交流变直流
Many electronic devices require DC, so rectification is used to convert AC into a unidirectional current. Half‑wave rectification uses a single diode, letting through only every other half‑cycle.
许多电子设备需要直流电，因此通过整流将交流电转换为单向电流。半波整流使用单个二极管，仅允许每隔半个周期的波形通过。
In full‑wave rectification, a bridge of four diodes steers both half‑cycles to produce a pulsating DC output with higher mean voltage.
在全波整流中，由四个二极管组成的桥式电路引导两个半周的波形，产生平均电压更高的脉动直流输出。
A capacitor connected across the load smooths the rectified output by charging when the voltage rises and discharging through the load when it falls, reducing ripple.
负载两端并联电容器可平滑整流输出：电压升高时充电，电压下降时经负载放电，从而减小纹波。
The smoothed DC voltage is approximately Vpeak minus some ripple, and the capacitor value determines the time constant τ = RC. A larger capacitance gives better smoothing but increases the initial charging surge.
平滑后的直流电压约等于峰值电压减去一定的纹波，电容值决定时间常数 τ = RC。电容越大平滑效果越好，但会增加初始充电浪涌电流。
IB HL candidates are expected to sketch and interpret rectifier circuits and the resulting voltage waveforms, linking them to the role of diodes and capacitors.
IB HL 考生应能绘制并解读整流电路及其输出电压波形，并将其与二极管和电容的作用相联系。
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