📚 IB CCEA Physics: Alternating Current | IB CCEA 物理：交流电 考点精讲
Alternating current (AC) is a cornerstone of modern electrical systems, appearing in every IB Physics syllabus under electromagnetic induction and AC circuit analysis. This article covers the essential concepts, equations, and problem-solving techniques you need for the CCEA and IB examinations – from sinusoidal waveforms and root‑mean‑square values to reactance, impedance, resonance and transformers.
交流电是现代电力系统的基石，出现在IB物理电磁感应与交流电路分析的每一个考点中。本文涵盖CCEA及IB考试所必需的核心概念、公式与解题技巧——从正弦波形与方均根值，到电抗、阻抗、谐振与变压器。
1. What is Alternating Current? | 什么是交流电？
Alternating current (AC) is an electric current that periodically reverses direction, unlike direct current (DC) which flows in a single direction. The voltage in an AC circuit also alternates sinusoidally in most mains supplies, described by the equation V = V₀ sin(ωt), where V₀ is the peak voltage and ω is the angular frequency.
交流电是指电流方向周期性反转的电流，与单向流动的直流电不同。在大多数市电中，电压也按正弦规律变化，可用方程 V = V₀ sin(ωt) 描述，其中 V₀ 为峰值电压，ω 为角频率。
2. Sinusoidal AC: Key Parameters | 正弦交流电的关键参数
A sinusoidal AC waveform is defined by its peak value V₀ (or I₀), period T, frequency f = 1/T, and angular frequency ω = 2πf. The instantaneous voltage v(t) = V₀ sin(ωt) and current i(t) = I₀ sin(ωt − φ) may be out of phase by an angle φ.
正弦交流波形由其峰值 V₀（或 I₀）、周期 T、频率 f = 1/T 以及角频率 ω = 2πf 定义。瞬时电压 v(t) = V₀ sin(ωt) 与电流 i(t) = I₀ sin(ωt − φ) 之间可能存在相位差 φ。
3. RMS and Peak Values | 有效值与峰值
The root‑mean‑square (rms) value of an AC current or voltage is the equivalent DC value that delivers the same average power to a resistor. For a sinusoidal waveform: Vrms = V₀/√2 and Irms = I₀/√2. Mains electricity is commonly quoted as 230 V rms (UK/Europe) or 120 V rms (US), meaning the peak voltage is about 325 V or 170 V respectively.
交流电流或电压的方均根值（有效值）是指能在电阻上产生相同平均功率的等效直流值。对于正弦波形：Vrms = V₀/√2，Irms = I₀/√2。市电电压通常标称为 230 V 有效值（英国/欧洲）或 120 V 有效值（美国），相应的峰值电压分别约为 325 V 与 170 V。
4. Mean Value of AC | 交流电的平均值
The average value of a full sinusoidal cycle is zero because the positive and negative half‑cycles cancel. The mean of the absolute value (rectified average) over a half‑cycle is Vavg = 2V₀/π. This is rarely used in power calculations but appears in some rectifier circuit contexts.
一个完整正弦波周期的平均值为零，因为正负半周期相互抵消。半波整流后的绝对平均值（整流平均值）为 Vavg = 2V₀/π。此值在功率计算中较少使用，但在一些整流电路分析中会出现。
5. Phasor Representation | 相量表示
Phasor diagrams treat alternating quantities as rotating vectors. The length of the vector represents the peak value (or rms), and the angle with the reference axis shows the phase. In a pure resistor, voltage and current phasors are in phase; in a capacitor, current leads voltage by 90°; in an inductor, current lags voltage by 90°.
相量图将交流量视为旋转矢量。矢量长度代表峰值（或有效值），与参考轴的夹角表示相位。在纯电阻中，电压与电流相量同相；在电容中，电流超前电压 90°；在电感中，电流滞后电压 90°。
6. Resistor in an AC Circuit | 交流电路中的电阻
A resistor obeys Ohm's law instantaneously: vR = iR R. The voltage and current are in phase, so the phasors are aligned. The power dissipated is P = Irms² R = Vrms² / R, all converted to heat.
电阻器时刻遵循欧姆定律：vR = iR R。电压与电流同相，相量对齐。消耗的功率为 P = Irms² R = Vrms² / R，全部转化为热量。
7. Capacitor in an AC Circuit: Capacitive Reactance | 交流电路中的电容：容抗
A capacitor opposes changes in voltage, causing the current to lead the voltage by 90°. Its capacitive reactance is XC = 1/(ωC) = 1/(2πf C), with units of ohms. The rms current and voltage are related by Vrms = Irms XC. No net power is dissipated – energy is stored and returned to the circuit.
电容器阻碍电压变化，使电流超前电压 90°。其容抗为 XC = 1/(ωC) = 1/(2πf C)，单位为欧姆。有效值电流与电压满足 Vrms = Irms XC。无净功率消耗——能量被储存并返回电路。
8. Inductor in an AC Circuit: Inductive Reactance | 交流电路中的电感：感抗
An inductor opposes changes in current, causing the current to lag the voltage by 90°. Its inductive reactance is XL = ωL = 2πf L, also in ohms. Again, Vrms = Irms XL. An ideal inductor dissipates no net power; it only exchanges energy with the magnetic field.
电感器阻碍电流变化，使电流滞后电压 90°。其感抗为 XL = ωL = 2πf L，单位也是欧姆。同样有 Vrms = Irms XL。理想电感不净耗散功率，仅与磁场交换能量。
9. Series LCR Circuit and Impedance | 串联LCR电路与阻抗
In a series LCR circuit, the total opposition to current is the impedance Z, given by Z = √(R² + (XL − XC)²). The phase angle φ between the total voltage and current satisfies tan φ = (XL − XC) / R. The rms current is Irms = Vrms / Z.
在串联LCR电路中，对电流的总阻碍为阻抗 Z，计算公式为 Z = √(R² + (XL − XC)²)。总电压与电流的相位角 φ 满足 tan φ = (XL − XC) / R。有效值电流为 Irms = Vrms / Z。
10. Resonance in AC Circuits | 交流电路中的谐振
Resonance occurs when XL = XC, i.e. ωL = 1/(ωC). The resonant frequency is f₀ = 1/(2π√LC) ximum, and the voltage across the inductor and capacitor can be many times greater than the supply voltage (voltage magnification).
当 XL = XC，即 ωL = 1/(ωC) 时发生谐振。谐振频率为 f₀ = 1/(2π√LC)。谐振时，阻抗呈现纯电阻性（Z = R），电流最大，电感和电容上的电压可能远大于电源电压（电压放大）。
11. Power in AC Circuits and Power Factor | 交流电功率与功率因数
Only the resistive part of an AC circuit dissipates average power. The average power is P = Vrms Irms cos φ e loads, cos φ = 0 and no net power is dissipated. The unit of real power is the watt (W).
交流电路中只有电阻部分消耗平均功率。平均功率为 P = Vrms Irms cos φ，其中 cos φ 称为功率因数。纯电阻负载的功率因数为 1；纯电抗负载的功率因数为 0，无净功率消耗。有功功率的单位是瓦特（W）。
12. Transformers | 变压器
A transformer uses two magnetically linked coils to change an AC voltage. For an ideal transformer: Vs / Vp = Ns / Np and Ip Vp = Is Vs (100% efficiency). Step‑up transformers increase voltage (Ns > Np), while step‑down transformers decrease voltage. Real transformers have small losses due to eddy currents, hysteresis and coil resistance.
变压器利用两个磁耦合线圈来改变交流电压。对于理想变压器：Vs / Vp = Ns / Np，且 Ip Vp = Is Vs（效率 100%）。升压变压器升高电压（Ns > Np），降压变压器降低电压。实际变压器因涡流、磁滞和线圈电阻而有少量损耗。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图