Alternating Currents in CIE A-Level Physics | CIE A-Level物理中的交流电

📚 Alternating Currents in CIE A-Level Physics | CIE A-Level物理中的交流电

An alternating current (AC) is an electric current that periodically reverses direction, in contrast to direct current (DC) which flows in only one direction. In A-Level physics, AC circuits are studied because most mains electricity is supplied as a sinusoidal alternating current, and understanding its behaviour is essential for power transmission and electronic circuits.

交流电（AC）是一种周期性改变方向的电流，与只沿一个方向流动的直流电（DC）形成对比。在A-Level物理中，研究交流电路是因为大多数市电以正弦交流电的形式供应，理解其行为对于电力传输和电子电路至关重要。

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1. What is an Alternating Current? | 什么是交流电？

An alternating current is defined as a current whose magnitude and direction vary periodically with time. The most common form is a sinusoidal alternating current, which can be represented by the equation:

交流电定义为大小和方向随时间周期性变化的电流。最常见的形式是正弦交流电，可以用方程表示：

I = I₀ sin(ωt)

where I is the instantaneous current at time t, I₀ is the peak (maximum) current, and ω is the angular frequency. The angular frequency is related to the frequency f by:

其中 I 是时间 t 时的瞬时电流，I₀ 是峰值（最大）电流，ω 是角频率。角频率与频率 f 的关系为：

ω = 2πf

In many countries, the mains frequency is 50 Hz, which gives an angular frequency of about 314 rad s⁻¹. The current alternates because the sine function changes sign every half cycle.

在许多国家，市电频率为50 Hz，对应的角频率约为314 rad s⁻¹。电流交替变化是因为正弦函数每半个周期改变一次符号。

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

The sinusoidal waveform of an AC voltage or current can be displayed on an oscilloscope. Key terms used to describe the waveform are:

交流电压或电流的正弦波形可以显示在示波器上。用于描述波形的关键术语有：

• Peak value (I₀ or V₀): the maximum value of current or voltage. | 峰值（I₀ 或 V₀）：电流或电压的最大值。
• Time period (T): the time taken for one complete cycle. | 周期（T）：完成一个完整循环所需的时间。
• Frequency (f): the number of cycles per second, equal to 1/T. | 频率（f）：每秒的循环次数，等于 1/T。
• Peak-to-peak value: twice the peak value, often measured from an oscilloscope trace. | 峰峰值：峰值的两倍，通常从示波器轨迹上测得。

The voltage waveform can also be written as V = V₀ sin(ωt), and the instantaneous power in a resistor depends on the square of the current or voltage.

电压波形也可写为 V = V₀ sin(ωt)，电阻中的瞬时功率取决于电流或电压的平方。

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3. Root-Mean-Square Values | 方均根值

Because an alternating current is zero at certain instants and maximum at others, its average over a full cycle is zero. To describe the effective heating effect of an AC, we use the root-mean-square (rms) value. The rms value of an alternating current is equal to the direct current that would dissipate the same average power in a given resistor.

由于交流电在某些时刻为零，在另一些时刻为最大值，它在一个完整周期内的平均值为零。为了描述交流电的有效热效应，我们使用方均根（rms）值。交流电的方均根值等于在给定电阻中耗散相同平均功率的直流电流。

For a sinusoidal current, the rms current is given by:

对于正弦电流，方均根电流由下式给出：

I_rms = I₀ / √2 ≈ 0.707 I₀

Similarly, the rms voltage is:

类似地，方均根电压为：

V_rms = V₀ / √2 ≈ 0.707 V₀

In the UK, the mains supply is often quoted as 230 V; this is the rms voltage. The peak voltage is therefore about 325 V because 230 × √2 ≈ 325 V.

在英国，市电电压通常标称为230 V；这是方均根电压。因此峰值电压约为325 V，因为 230 × √2 ≈ 325 V。

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4. Power Dissipation in AC Circuits | 交流电路中的功率耗散

For a purely resistive AC circuit, the instantaneous power is P = I²R = V²/R. The average power over a complete cycle can be calculated using rms values:

对于纯电阻交流电路，瞬时功率为 P = I²R = V²/R。一个完整周期内的平均功率可以使用方均根值计算：

P_avg = I_rms² R = V_rms² / R = I_rms V_rms

This is why rms values are so useful: they allow us to use the same power formulas as in DC circuits. If a resistor carries an alternating current with a peak value of 2 A, its rms current is 1.41 A, and the average power dissipated is (1.41 A)² × R.

这就是方均根值如此有用的原因：它们允许我们使用与直流电路相同的功率公式。如果一个电阻器通过峰值为2 A的交流电，其方均根电流为1.41 A，则耗散的平均功率为 (1.41 A)² × R。

For non-resistive components such as capacitors or inductors, the average power may be zero because the current and voltage are out of phase by 90°, so no net energy is dissipated over a full cycle.

对于电容器或电感器等非电阻性元件，平均功率可能为零，因为电流和电压相位相差90°，因此在一个完整周期内没有净能量耗散。

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5. AC and Resistors: Phase Relationship | 交流电与电阻：相位关系

In a purely resistive AC circuit, the current and voltage are in phase. This means that when the voltage reaches its maximum positive value, the current also reaches its maximum positive value at the same instant. The waveforms cross the time axis together.

在纯电阻交流电路中，电流和电压同相。这意味着当电压达到其正最大值时，电流也在同一时刻达到正最大值。波形同时穿过时间轴。

On a phasor diagram, the voltage and current phasors rotate at the same angular frequency and remain aligned. The resistance R is defined as the ratio of the rms voltage to the rms current, just as in DC circuits:

在相量图上，电压和电流相量以相同的角频率旋转并保持对齐。电阻 R 定义为方均根电压与方均根电流之比，和直流电路一样：

R = V_rms / I_rms

No phase difference means the power factor is 1, and the average power is simply I_rms V_rms.

没有相位差意味着功率因数为1，平均功率就是 I_rms V_rms。

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6. AC and Capacitors: Capacitive Reactance | 交流电与电容：容抗

A capacitor in an AC circuit does not allow a steady direct current to flow, but an alternating current can charge and discharge the capacitor

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

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