📚 IB & OCR Physics: Mastering Alternating Current | IB OCR 物理：交流电 考点精讲
Alternating current (AC) is a fundamental concept in both IB and OCR A-Level Physics, playing a crucial role in power generation, transmission, and everyday electronics. Understanding AC involves grasping sinusoidal waveforms, root-mean-square (RMS) values, phase relationships in reactive components, and practical applications such as transformers and rectification. This comprehensive revision guide covers key concepts, equations, and common exam pitfalls to help you master AC theory for your exams.
交流电(AC) 是IB和OCR A-Level物理中的基础内容，在发电、输电及日常电子设备中起着至关重要的作用。理解交流电需要掌握正弦波形、均方根(RMS) 值、电抗元件中的相位关系，以及变压器和整流等实际应用。本综合复习指南涵盖核心概念、关键公式及常见考试陷阱，助你在考试中攻克交流电理论。
1. Understanding Alternating Current (AC) | 理解交流电 (AC)
Alternating current differs from direct current because its magnitude and direction change periodically with time. The most common waveform is sinusoidal, described by V(t) = Vmax sin(ωt + φ), where Vmax is the peak voltage, ω the angular frequency, and φ the phase constant.
交流电与直流电的区别在于其大小和方向随时间周期变化。最常见的波形为正弦波，用 V(t) = Vmax sin(ωt + φ) 描述，其中 Vmax 为峰值电压，ω 为角频率，φ 为初相。
AC is produced by rotating coils in a magnetic field (generators), obeying Faraday’s law of electromagnetic induction. The induced EMF is sinusoidal when the coil rotates at constant angular velocity.
交流电由磁场中旋转的线圈（发电机）产生，遵循法拉第电磁感应定律。当线圈以恒定角速度旋转时，感应电动势为正弦形式。
In diagrams, AC is shown as a sine wave crossing the time axis, while DC is a straight horizontal line. The key feature of AC is that its average value over a full cycle is zero, but its heating effect is non-zero.
在图像中，交流电表示为穿过时间轴的正弦波，而直流电为一条水平直线。交流电的关键特征是，一个完整周期内的平均值为零，但其热效应不为零。
2. Sinusoidal Waveform and Key Parameters | 正弦波形及其关键参数
The time period T is the time for one complete cycle, and the frequency f = 1/T. Angular frequency ω = 2πf = 2π/T. For mains electricity, typical values are f = 50 Hz (Europe) or 60 Hz (USA), T = 20 ms or 16.7 ms respectively.
周期 T 是完成一个完整循环所需的时间，频率 f = 1/T。角频率 ω = 2πf = 2π/T。对于市电，典型频率为 f = 50 Hz (欧洲) 或 60 Hz (美国)，对应周期 T = 20 ms 或 16.7 ms。
The peak voltage Vmax (often written V0) is the maximum magnitude of the voltage. Peak-to-peak voltage Vpp = 2Vmax. Instantaneous voltage v = Vmax sin(ωt). Similarly, instantaneous current i = Imax sin(ωt) for a purely resistive load.
峰值电压 Vmax (常写作 V0) 是电压的最大幅度。峰峰值电压 Vpp = 2Vmax。瞬时电压 v = Vmax sin(ωt)。类似地，对于纯阻性负载，瞬时电流 i = Imax sin(ωt)。
When two AC quantities are compared, their phase difference is measured in degrees or radians. In-phase means 0° difference; anti-phase is 180°.
当比较两个交流量时，它们的相位差用度或弧度计量。同相意味着 0° 差；反相为 180°。
3. Root Mean Square (RMS) Values | 均方根 (RMS) 值
The RMS value of an alternating quantity is the equivalent DC value that produces the same heating effect in a resistor. For sinusoidal AC: Vrms = Vmax / √2, Irms = Imax / √2. The derivation involves squaring, taking mean, and square root.
交流电量的均方根值，是能在电阻中产生相同热效应的等效直流值。对于正弦交流电：Vrms = Vmax / √2，Irms = Imax / √2。其推导涉及平方、取平均、再开方。
RMS is used for power calculations and multimeter readings. For a UK mains 230 V supply, this is the RMS voltage; the peak voltage is about 325 V. Always check whether a given voltage is peak or RMS in exam questions.
RMS 值用于功率计算和万用表读数。英国 230 V 市电指的是 RMS 电压；其峰值电压约为 325 V。考题中务必确认所给电压是峰值还是 RMS 值。
The RMS value is not √2 times the average; the average of a full-cycle sine wave is zero. For half-wave rectified sine, Vrms = Vmax / 2.
RMS 值并非平均值的 √2 倍；一个完整正弦波的平均值为零。对于半波整流正弦波，Vrms = Vmax / 2。
4. AC Power and Average Power | 交流电功率与平均功率
In a purely resistive circuit, power dissipated p(t) = v(t) i(t). The average power Pavg = Irms Vrms = Irms² R = Vrms² / R. Because p(t) fluctuates at twice the supply frequency, the average is half the peak power.
在纯电阻电路中，瞬时功率 p(t) = v(t) i(t)。平均功率 Pavg = Irms Vrms = Irms² R = Vrms² / R。由于瞬时功率以两倍电源频率波动，平均值是峰值功率的一半。
The rms values allow the use of familiar DC power equations for AC, simplifying circuit analysis. However, for circuits with inductance or capacitance, the average power also depends on the power factor cos φ.
使用 RMS 值后，熟悉的直流功率公式可应用于交流电，简化了电路分析。然而，对于包含电感或电容的电路，平均功率还取决于功率因数 cos φ。
Power factor = cos φ = R / Z. Only resistive components dissipate net power; ideal inductors and capacitors store and return energy.
功率因数 = cos φ = R / Z。只有电阻性元件消耗净功率；理想电感和电容储能并返还能量。
5. AC in Resistors: Purely Resistive Circuit | 交流电在电阻中：纯电阻电路
In a resistor, current and voltage are in phase. Phasors rotate together. The impedance is simply the resistance R, and the current Irms = Vrms / R.
在电阻中，电流与电压同相。相量同步旋转。阻抗即为电阻 R，电流 Irms = Vrms / R。
No phase shift means power factor is 1, and all electric energy is converted to heat. The waveform of instantaneous power is always positive, showing continuous energy dissipation.
没有相位差意味着功率因数为 1，所有电能都转化为热能。瞬时功率的波形始终为正，表明能量持续耗散。
6. AC in Capacitors: Capacitive Reactance | 交流电在电容中：容抗
A capacitor in an AC circuit provides reactance XC = 1 / (ωC) = 1 / (2πfC). The unit is ohm (Ω). As frequency increases, capacitive reactance decreases, so a capacitor passes high-frequency signals more easily.
交流电路中的电容器提供容抗 XC = 1 / (ωC) = 1 / (2πfC)，单位是欧姆 (Ω)。频率增加，容抗减小，因此电容更容易通过高频信号。
The current leads the voltage by 90° (π/2 rad). This is remembered by the mnemonic ‘CIVIL’: in a Capacitor, I leads V; in an inductor, V leads I.
电流超前电压 90° (π/2 rad)。记忆口诀 ‘CIVIL’：电容 (C) 中 I 超前 V；电感 (L) 中 V 超前 I (I lagging V)。
At very high frequencies, a capacitor behaves almost like a short circuit; at very low frequencies (or DC), it acts as an open circuit.
在很高频率下，电容近似短路；在很低频率（或直流）下，它相当于开路。
7. AC in Inductors: Inductive Reactance | 交流电在电感中：感抗
Inductive reactance XL = ωL = 2πfL. It increases with frequency. At high frequencies, an inductor acts almost as an open circuit because its reactance becomes very large.
感抗 XL = ωL = 2πfL，随频率增大而增加。高频时电感近似开路，因为其感抗变得非常大。
The voltage leads the current by 90° (π/2). In a purely inductive circuit, no net power is dissipated because energy stored in the magnetic field returns to the circuit each cycle.
电压超前电流 90° (π/2)。在纯电感电路中，因为磁场储能每周期返还电路，所以没有净功率消耗。
At low frequencies, an inductor offers little opposition, behaving almost like a wire (short).
在低频时，电感阻碍很小，几乎像一根导线（短路）。
8. RC
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