IB Edexcel Physics: AC Circuit Essentials | IB Edexcel 物理：交流电考点精讲

📚 IB Edexcel Physics: AC Circuit Essentials | IB Edexcel 物理：交流电考点精讲

Alternating current (AC) is a fundamental topic in both IB and Edexcel A-Level Physics, underpinning much of modern electrical technology. Understanding AC circuits, phasor analysis, reactance, impedance, power factor and transformers is essential for mastering electricity and magnetism.

交流电（AC）是 IB 和 Edexcel A-Level 物理中的核心主题，是现代电气技术的重要基础。掌握交流电路、相量分析、容抗感抗、阻抗、功率因数以及变压器是精通电磁学的关键。

1. AC vs DC Current | 交流电与直流电

Direct current (DC) flows steadily in one direction, while alternating current (AC) periodically reverses direction. AC is generated by rotating a coil in a magnetic field, as in an alternator, producing a sinusoidal output. In an AC circuit, the voltage and current vary with time as V = V₀ sin(ωt) and I = I₀ sin(ωt), where V₀ and I₀ are peak values, and ω = 2πf is the angular frequency.

直流电（DC）始终沿一个方向流动，而交流电（AC）则周期性地改变方向。交流电由线圈在磁场中旋转产生，如同交流发电机，输出正弦波形。在交流电路中，电压和电流随时间变化为 V = V₀ sin(ωt) 和 I = I₀ sin(ωt)，其中 V₀ 和 I₀ 为峰值，ω = 2πf 是角频率。

AC is preferred for power distribution because its voltage can be easily stepped up or down using transformers, minimising transmission losses.

交流电更适合输电，因为可以通过变压器方便地升降电压，从而最大限度减少传输损耗。

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

The standard AC waveform is a sine wave. Instantaneous voltage is given by v(t) = V₀ sin(2πft). The period T = 1/f, and the frequency f is measured in hertz (Hz). The angular frequency ω = 2πf has units of rad/s. On an oscilloscope, you can measure the peak voltage and the time period directly.

标准交流波形为正弦波，瞬时电压由 v(t) = V₀ sin(2πft) 给出。周期 T = 1/f，频率 f 单位为赫兹（Hz）。角频率 ω = 2πf，单位为弧度/秒。在示波器上，可以直接测量峰值电压和周期。

In exams, you must be able to read these values from a graph and convert between peak, rms, and peak-to-peak quantities.

在考试中，你必须能够从图像中读取这些值，并在峰值、有效值与峰峰值之间进行转换。

3. Peak, Peak-to-Peak, and Average Values | 峰值、峰峰值与平均值

The peak value V₀ is the maximum voltage. The peak-to-peak voltage V_pp is twice the peak: V_pp = 2V₀. Over a complete cycle, the average of a pure sinusoidal voltage is zero because the positive and negative halves cancel; however, the average of the absolute value is (2/π) V₀.

峰值 V₀ 是最大电压值。峰峰值 V_pp 是峰值的两倍：V_pp = 2V₀。在整个周期内，纯正弦电压的平均值为零，因为正半周与负半周互相抵消；但绝对值的平均值则是 (2/π) V₀。

These distinctions are important when studying rectified signals, where the average value relates to the DC component.

这些区别在研究整流信号时很重要，平均值与该信号的直流分量相关。

4. Root Mean Square (RMS) Value | 有效值（均方根值）

The RMS value of an AC voltage or current is the equivalent steady DC value that would deliver the same average power to a resistor. For a sinusoidal waveform, V_rms = V₀/√2 and I_rms = I₀/√2. This arises because P_avg = I_rms²R = V_rms²/R.

交流电压或电流的有效值（RMS）是对电阻能提供相同平均功率的等效直流值。对于正弦波形，V_rms = V₀/√2，I_rms = I₀/√2。这源自于 P_avg = I_rms²R = V_rms²/R。

For example, the UK mains is 230 V rms, corresponding to a peak of about 325 V. Always identify whether a problem states peak or rms values before calculating power or current.

例如，英国市电为 230 V 有效值，对应的峰值约 325 V。在计算功率或电流之前，务必识别题目给出的是峰值还是有效值。

5. AC Circuits with Resistors | 纯电阻交流电路

In a purely resistive AC circuit, current and voltage are in phase. Ohm’s law applies for instantaneous values: v = iR. The resistance R is independent of frequency, and the average power dissipated is P = I_rmsV_rms because the power factor is 1.

在纯电阻交流电路中，电流与电压同相。欧姆定律适用于瞬时值：v = iR。电阻 R 与频率无关，且消耗的平均功率为 P = I_rmsV_rms，因为功率因数为 1。

This behaviour is identical to that in DC circuits, except that the instantaneous values continuously change.

这种行为与直流电路完全相同，只是瞬时值在不断变化。

6. AC Circuits with Capacitors | 纯电容交流电路

When a capacitor is connected to an AC supply, the voltage lags behind the current by 90° (π/2 rad). The capacitive reactance is X_C = 1/(ωC) = 1/(2πfC), which is high at low frequencies and low at high frequencies. A handy memory aid is ‘CIVIL’: in a Capacitor (C), I leads V (I before V).

电容器接入交流电源时，电压滞后电流 90°（π/2 弧度）。容抗为 X_C = 1/(ωC) = 1/(2πfC)，低频时容抗大，高频时容抗小。一个方便的记忆技巧是 ‘CIVIL’：在电容器（C）中，I 超前 V。

No net power is dissipated in an ideal capacitor; energy is stored in the electric field during one quarter-cycle and returned in the next.

Published by TutorHao | IB Physics Revision Series | aleveler.com

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