AS Physics: Alternating Current In-Depth Revision | AS 物理：交流电考点精讲

📚 AS Physics: Alternating Current In-Depth Revision | AS 物理：交流电考点精讲

Alternating current (AC) is a cornerstone topic in AS Physics, connecting electromagnetic induction, circuit theory, and practical electronics. This guide systematically covers every key concept – from sinusoidal waveforms and r.m.s. values to transformers and rectification – exactly as required by major exam boards.

交流电是 AS 物理的核心专题，连接着电磁感应、电路理论与实际电子技术。本文系统梳理所有关键考点——从正弦波形和有效值到变压器与整流——精准对应各大考试局要求。

1. Understanding AC and DC | 理解交流电与直流电

Direct current (DC) flows in one fixed direction, producing a steady voltage across a resistor. In contrast, alternating current (AC) periodically reverses its direction of flow, causing the voltage to change polarity over time.

直流电 (DC) 沿一个固定方向流动，在电阻上产生稳定电压。而交流电 (AC) 则周期性地改变流动方向，使得电压随时间反转极性。

In AS Physics, we focus on sinusoidal AC, which can be generated by rotating a coil in a uniform magnetic field. This simple generator principle links the topic directly to Faraday’s law of electromagnetic induction.

在 AS 物理中，我们重点研究正弦交流电，它可以通过线圈在匀强磁场中旋转产生。这一简单的发电原理将本专题与法拉第电磁感应定律直接挂钩。

The graph of voltage or current against time for sinusoidal AC is a smooth sine or cosine curve. The shape reflects how the coil cuts magnetic flux at a varying rate as it rotates.

正弦交流电的电压或电流随时间变化的图像是一条光滑的正弦或余弦曲线，这种形状反映了线圈旋转时切割磁通量的速率不断变化。

2. Sinusoidal Waveform and the Rotating Coil | 正弦波形与旋转线圈

When a rectangular coil of area A, with N turns, rotates at constant angular velocity ω in a uniform magnetic flux density B, the induced e.m.f. varies as ε = BANω sin(ωt). The peak e.m.f. is ε₀ = BANω, and the instantaneous value can be written as ε = ε₀ sin(ωt) if timing starts from the zero-crossing.

当面积为 A 的 N 匝矩形线圈在匀强磁场 B 中以恒定角速度 ω 旋转时，产生的感应电动势按 ε = BANω sin(ωt) 变化。峰值电动势为 ε₀ = BANω，若从过零点开始计时，瞬时值可写为 ε = ε₀ sin(ωt)。

Similar equations hold for current and voltage in a purely resistive circuit: I = I₀ sin(ωt) and V = V₀ sin(ωt). The sinusoidal shape is universal for rotating-coil generators.

对于纯电阻电路，电流和电压有类似方程：I = I₀ sin(ωt) 和 V = V₀ sin(ωt)。正弦波形是旋转线圈发电机的普遍特征。

An oscilloscope display of an AC signal shows a repeating smooth wave that crosses zero twice per cycle. The time base setting allows you to measure the period T directly, while the Y-gain setting reveals the peak voltage V₀.

示波器上显示的交流信号呈现每周期两次穿越零点的重复光滑波形。时基旋钮可让你直接测量周期 T，而 Y 增益旋钮则显示峰值电压 V₀。

3. Key Quantities: Period, Frequency and Angular Frequency | 关键物理量：周期、频率与角频率

The period T is the time taken for one complete cycle of the AC waveform. Frequency f, measured in hertz (Hz), is the number of cycles per second: f = 1 / T.

周期 T 是交流波形完成一个完整循环所需的时间。频率 f 以赫兹 (Hz) 为单位，表示每秒的循环数：f = 1 / T。

Angular frequency ω (omega) links rotational motion to the sinusoidal equation: ω = 2πf = 2π / T. Its unit is rad s⁻¹. The argument of the sine function, ωt, is in radians.

角频率 ω 将圆周运动与正弦方程联系起来：ω = 2πf = 2π / T，单位为 rad s⁻¹。正弦函数的自变量 ωt 以弧度为单位。

For typical mains electricity in the UK, f = 50 Hz, so T = 20 ms, and ω = 100π rad s⁻¹ ≈ 314 rad s⁻¹. These numbers often appear in exam calculations.

以英国市电为例，f = 50 Hz，因此 T = 20 ms，ω = 100π rad s⁻¹ ≈ 314 rad s⁻¹。这些数据常在考试计算题中出现。

V = V₀ sin(2πft) = V₀ sin(ωt)

4. Peak, Peak-to-Peak and Instantaneous Values | 峰值、峰峰值与瞬时值

The peak value (V₀ or I₀) is the maximum amplitude of the wave. It is directly read from an oscilloscope screen using the Y-gain setting. Peak-to-peak value is twice the peak: Vₚₚ = 2V₀.

峰值 (V₀ 或 I₀) 是波形的最大振幅，可直接通过示波器的 Y 增益设置读取。峰峰值是峰值的两倍：Vₚₚ = 2V₀。

The instantaneous value v or i is the value at a specific moment t. For sine waves, v = V₀ sin(ωt). Knowing the argument ωt lets you calculate the exact voltage at any instant.

瞬时值 v 或 i 是某个具体时刻 t 的数值。对正弦波，v = V₀ sin(ωt)。知道 ωt 后即可计算任意时刻的准确电压。

When describing an AC supply, specifying the peak voltage alone is insufficient; the effective heating capability is better described by the r.m.s. value.

描述交流电源时，仅给出峰值电压是不够的；其有效加热能力更适合用均方根值 (r.m.s.) 来描述。

5. Root-Mean-Square (r.m.s.) Value | 均方根值（有效值）

The r.m.s. value of an AC is the equivalent DC value that would dissipate the same power in a resistor. For a sinusoidal voltage or current, Vrms = V₀ / √2 and Irms = I₀ / √2.

交流电的有效值 (r.m.s.) 是与它能在电阻中产生相同发热功率的等效直流值。对于正弦电压或电流，Vrms = V₀ / √2，Irms = I₀ / √2。

Derivation: Power ∝ V², so the mean of V² over a complete cycle is V₀²/2. Taking the square root gives Vrms = V₀ / √2. The factor 1/√2 ≈ 0.707 is fundamental.

推导：功率正比于 V²，整个周期内 V² 的平均值为 V₀²/2。开平方即得 Vrms = V₀ / √2。因子 1/√2 ≈ 0.707 是基础常数。

In the UK, the declared mains voltage is 230 V r.m.s., which implies a peak voltage of about 325 V. Whenever you plug in a device, the insulation must withstand this peak, not just the r.m.s. value.

英国标称的市电电压为 230 V 有效值，这意味着峰值电压约为 325 V。每次插入电器时，其绝缘必须能承受此峰值，而不仅仅是有效值。

Vrms = V₀ / √2 Irms = I₀ / √2

6. Average Value of a Sinusoidal Waveform | 正弦波形的平均值

Over a full cycle, the average (mean) value of a symmetrical sinusoidal AC is zero, because the positive and negative halves cancel. This is why a moving-coil meter connected directly to AC reads zero.

在一个完整周期内，对称正弦交流电的平均值为零，因为正负半周相互抵消。这就是直接接入交流电的动圈式仪表读数为零的原因。

For rectification calculations, we often use the average of the full-wave rectified signal, which is 2V₀/π ≈ 0.637V₀. Half-wave rectification gives half of that: V₀/π.

在整流计算中，我们常用全波整流信号的平均值，即 2V₀/π ≈ 0.637V₀。半波整流的平均值则为其一半：V₀/π。

These average values appear in determining the DC component after rectification and before smoothing. Do not confuse average with r.m.s.; they have different physical meanings.

这些平均值用于确定整流后、平滑前的直流分量。不要将平均值与有效值混淆，它们具有不同的物理含义。

7. Power Dissipation in a Resistive Load | 纯电阻负载中的功率

In a purely resistive circuit, the instantaneous power is p = vi = V₀I₀ sin²(ωt). The average power over a cycle is P_avg = (V₀I₀)/2 = Vrms × Irms.

在纯电阻电路中，瞬时功率为 p = vi = V₀I₀ sin²(ωt)。一个周期内的平均功率 P_avg = (V₀I₀)/2 = Vrms × Irms。

Using Ohm’s law, we can express average power as P_avg = Irms² R = Vrms² / R. This is exactly the same form as the DC power formula, which justifies using r.m.s. values.

利用欧姆定律，平均功率可表达为 P_avg = Irms² R = Vrms² / R。这与直流功率公式形式完全一致，这正是使用有效值的理由。

Exam tip: When calculating energy consumption or heating, always use r.m.s. values unless the question explicitly asks for peak or instantaneous power.

考试提示：计算能量消耗或发热时，务必使用有效值，除非题目明确要求峰值功率或瞬时功率。

P_avg = Vrms Irms = Irms² R = Vrms² / R

8. The Ideal Transformer | 理想变压器

A transformer consists of two coils wound on a laminated soft-iron core. An alternating current in the primary coil creates a changing magnetic flux, which induces an e.m.f. in the secondary coil.

变压器由绕在叠片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，从而在次级线圈中感应出电动势。

For an ideal transformer (100% efficiency), the ratio of voltages equals the ratio of turns: Vₚ / Vₛ = Nₚ / Nₛ. A step-up transformer has Nₛ > Nₚ, while a step-down transformer has Nₛ < Nₚ.

对于理想变压器（效率 100%），电压比等于匝数比：Vₚ / Vₛ = Nₚ / Nₛ。升压变压器 Nₛ > Nₚ，降压变压器 Nₛ < Nₚ。

Power in equals power out: Vₚ Iₚ = Vₛ Iₛ, so Iₚ / Iₛ = Vₛ / Vₚ = Nₛ / Nₚ. Thus a step-up transformer decreases current, reducing I²R losses in transmission lines.

输入功率等于输出功率：Vₚ Iₚ = Vₛ Iₛ，因此 Iₚ / Iₛ = Vₛ / Vₚ = Nₛ / Nₚ。所以升压变压器会降低电流，从而减少输电线上的 I²R 损耗。

Real transformers have small energy losses due to eddy currents, hysteresis, and copper resistance. Laminating the core and using soft iron reduce these effects.

实际变压器因涡流、磁滞和铜电阻而有少量能量损耗。叠片铁芯和使用软铁可减少这些影响。

Vₚ / Vₛ = Nₚ / Nₛ Iₚ / Iₛ = Nₛ / Nₚ

9. Half-Wave Rectification | 半波整流

Half-wave rectification uses a single diode to allow current to flow only during the positive half-cycles of the AC input. The negative half-cycles are blocked, producing a pulsed DC output.

半波整流使用一个二极管，仅允许交流输入的正半周通过。负半周被阻断，产生脉动直流输出。

The output waveform consists of half-sine pulses. Its average DC value is V₀/π, and its r.m.s. value is V₀/2, both significantly lower than the input r.m.s. This makes half-wave rectification inefficient.

输出波形由半个正弦脉冲组成。其平均直流值为 V₀/π，有效值为 V₀/2，均远低于输入有效值，这使得半波整流效率较低。

The circuit is simple and cheap, but the large gaps between pulses cause significant ripple. Adding a reservoir capacitor smooths the output, but the ripple remains larger than in full-wave designs.

电路简单且廉价，但脉冲之间的大间隙导致较大纹波。添加滤波电容器可平滑输出，但纹波仍比全波设计大。

10. Full-Wave Rectification and Smoothing | 全波整流与滤波

A bridge rectifier uses four diodes to direct both positive and negative half-cycles into the load with the same polarity. The output waveform has twice as many pulses per cycle compared to half-wave.

桥式整流器使用四只二极管，将正、负半周均以同一极性引导至负载。与半波相比，其输出波形每周期脉冲数量加倍。

For a full-wave rectified sine wave, the average DC value is 2V₀/π ≈ 0.637V₀, and the r.m.s. value is V₀/√2, which is the same as the original AC r.m.s. before the diode drops.

对于全波整流正弦波，平均直流值为 2V₀/π ≈ 0.637V₀，有效值为 V₀/√2，若忽略二极管压降，与原始交流有效值相同。

A large capacitor connected across the output charges to the peak voltage and discharges slowly through the load, reducing ripple. The ripple voltage decreases with larger capacitance and higher load resistance.

并联在输出端的大电容充电至峰值电压，并经过负载缓慢放电，从而减小纹波。纹波电压随电容增大和负载电阻增高而降低。

The combination of full-wave rectifier and smoothing capacitor turns AC into nearly steady DC, used in power supplies for electronic devices. Exam questions often ask you to sketch waveforms before and after smoothing.

全波整流配合滤波电容可将交流电转化为近似平稳的直流电，用于电子设备电源。试题常要求画出平滑前后的波形草图。

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AS Physics: Alternating Current In-Depth Revision | AS 物理：交流电 考点精讲