Voltage: Physical Meaning and Measurement | 电压的物理意义与测量

📚 Voltage: Physical Meaning and Measurement | 电压的物理意义与测量

In IB Physics, voltage — more formally called electric potential difference — is one of the most fundamental ideas in electromagnetism. Yet many students confuse it with current, energy, or simply “push”. This article clarifies what voltage really means, where it comes from, and how it is measured in the laboratory.

在IB物理中，电压——更正式的名称为电势差——是电磁学中最基本的概念之一。然而许多学生将其与电流、能量或简单的“推动力”混淆。本文旨在阐明电压的真正含义、来源以及如何在实验室中进行测量。

1. Voltage as Work per Unit Charge | 电压：单位电荷所做的功

Voltage between two points is defined as the work done per unit positive charge moved from one point to the other against the electric field. The SI unit is the volt (V), where 1 V = 1 J C⁻¹.

两点之间的电压定义为：将单位正电荷在电场中从一点移动到另一点所做的功。国际单位是伏特（V），即 1 V = 1 J C⁻¹。

V = W / q

Here, W is the work done on the charge q. Voltage does not depend on the path taken, only on the positions of the two points in an electrostatic field.

其中 W 是对电荷 q 所做的功。在静电场中，电压不依赖于路径，只取决于两点的位置。

2. Electric Potential Energy | 电势能

A charge in an electric field possesses electric potential energy. When the charge moves through a potential difference, its potential energy changes by ΔEp = qΔV. This energy can be converted into kinetic energy, light, heat, or other forms.

电场中的电荷具有电势能。当电荷通过电势差移动时，其电势能变化为 ΔEp = qΔV。这种能量可以转化为动能、光、热或其他形式。

For example, as an electron (q = -1.6 × 10⁻¹⁹ C) accelerates through a potential difference of 1 V, it gains a kinetic energy of 1 electronvolt (1 eV = 1.6 × 10⁻¹⁹ J).

例如，当一个电子（q = -1.6 × 10⁻¹⁹ C）通过 1 V 的电势差加速时，它获得 1 电子伏特（1 eV = 1.6 × 10⁻¹⁹ J）的动能。

3. Voltage, Field and Distance | 电压、电场与距离

In a uniform electric field, the potential difference between two parallel plates is related to the electric field strength E and the separation d by:

在匀强电场中，两平行板之间的电势差与电场强度 E 和间距 d 的关系为：

E = V / d

Thus the electric field can be measured in volts per metre (V m⁻¹), equivalent to newtons per coulomb (N C⁻¹). The direction of the field is from high potential to low potential.

因此电场强度的单位可为伏特每米（V m⁻¹），与牛顿每库仑（N C⁻¹）等价。电场方向从高电势指向低电势。

4. Potential Difference vs. Electric Potential | 电势差与电势

Electric potential V at a point is the work done per unit charge in bringing a positive test charge from infinity to that point. Potential difference is the difference between two potentials. The absolute potential at infinity is defined as zero.

某点的电势 V 是指将正试探电荷从无穷远移到该点所做的功除以电荷量。电势差是两个电势之差。无穷远处的电势定义为 0。

Important: voltages in circuits are always potential differences. A voltmeter measures the difference between two points, not an absolute “amount of electricity”.

重要：电路中的电压总是电势差。伏特表测量的是两点之差，而不是某种绝对的“电量”。

5. The Voltmeter: Ideal and Real | 伏特表：理想与现实

A voltmeter is connected in parallel with the component whose voltage is to be measured. An ideal voltmeter would have infinite resistance so that it draws no current from the circuit and does not alter the voltage it is measuring.

伏特表应与被测元件并联连接。理想伏特表的电阻应为无穷大，这样它不会从电路中分走电流，也不会改变所测量的电压。

Real voltmeters have finite resistance, typically large compared to circuit resistances. If the voltmeter’s resistance is too low, it loads the circuit and the measured value becomes significantly smaller than the true value.

实际伏特表的电阻是有限的，但通常远大于电路中的电阻。如果伏特表电阻太小，它会对电路产生负载效应，使测得值明显小于真实值。

6. Connecting the Voltmeter Correctly | 正确连接伏特表

To measure the voltage across a resistor R in a circuit:

要测量电路中电阻 R 两端的电压：

Connect the voltmeter in parallel with R.

将伏特表与 R 并联连接。
Connect the positive terminal of the voltmeter to the side at higher potential (the side closer to the positive terminal of the battery).

将伏特表的正接线柱接在高电势一侧（靠近电池正极的一侧）。
Record the reading once the circuit is complete.

电路闭合后读取示数。

Incorrect polarity causes the needle of an analogue meter to deflect in the wrong direction, or a digital metre to show a negative value.

极性接反会使模拟式电表指针向错误方向偏转，或使数字电表显示负值。

7. Voltage in Series and Parallel Circuits | 串联与并联电路中的电压

In a series circuit, the total voltage supplied by the source is divided among the components. The sum of potential differences across each component equals the source voltage:

在串联电路中，电源提供的总电压分配给各元件。每个元件两端电势差之和等于电源电压：

V_total = V₁ + V₂ + V₃ + …

In a parallel circuit, every branch has the same potential difference. The voltage across each branch equals the battery voltage.

在并联电路中，每条支路两端具有相同的电势差。每条支路两端的电压都等于电池电压。

8. EMF vs. Terminal Potential Difference | 电动势与端电压

Electromotive force (EMF) is the total energy supplied by a battery per unit charge, denoted ε. A real battery has internal resistance r. When current I flows, part of the energy is lost inside the battery as heat, so the terminal voltage V = ε − Ir.

电动势（EMF）是电池每单位电荷所提供的总能量，记为 ε。实际电池具有内阻 r。当电流 I 流过时，部分能量在电池内部以热量形式损失，因此端电压为 V = ε − Ir。

V = ε − I r

When no current is drawn (open circuit), the terminal voltage equals the EMF. As current increases, terminal voltage decreases.

当不输出电流（开路）时，端电压等于电动势。电流增大时，端电压降低。

9. Measuring EMF and Internal Resistance | 测量电动势与内阻

A common IB experiment measures the EMF and internal resistance of a cell using a variable resistor and a voltmeter connected across the cell terminals. By varying the current and recording corresponding terminal voltage, a graph of V against I is plotted.

一个常见的IB实验使用滑动变阻器和并联在电池两端的伏特表来测量电池的电动势和内阻。通过改变电流并记录相应的端电压，绘制 V-I 图。

The y-intercept gives ε, and the negative slope gives r. This is because the graph obeys V = −rI + ε.

纵轴截距给出 ε，斜率的绝对值给出 r。因为图线满足 V = −rI + ε。

10. Measuring Potential Difference in Electric Fields | 电场中电势差的测量

In electrostatics experiments, a voltmeter can measure the potential difference between two points in a field, for example between two conducting plates connected to a power supply. Equipotential lines can be mapped using a probe connected to a voltmeter.

在静电实验中，伏特表可以测量电场中两点间的电势差，例如连接电源的两块导体板之间的电势差。可以使用连接到伏特表的探针描绘等势线。

An equipotential line is a set of points where the potential is the same. No work is done in moving a charge along an equipotential line.

等势线是电势相同的点所构成的线。沿等势线移动电荷不需要做功。

11. AC and DC Voltage | 交流电压与直流电压

Direct current (DC) voltage has a constant polarity and magnitude over time. Alternating current (AC) voltage changes direction periodically. The household mains supply in most countries provides an RMS voltage of about 230 V at 50 Hz.

直流（DC）电压的极性和大小随时间保持恒定。交流（AC）电压周期性改变方向。大多数国家的家庭市电提供约 230 V（有效值）、频率 50 Hz 的交流电压。

An average-reading multimeter measures rectified average, while true-RMS voltmeters are required for accurate measurements of non-sinusoidal waveforms.

普通平均值响应的万用表测量整流后的平均值，若要准确测量非正弦波形，需要使用真有效值（true-RMS）伏特表。

12. Common Mistakes and Exam Tips | 常见错误与考试要点

Do not say “voltage is energy” — voltage is energy per unit charge. Energy is ΔEp = qV.

不要说“电压就是能量”——电压是单位电荷的能量。能量为 ΔEp = qV。
Never connect a voltmeter in series. It would have extremely high resistance and effectively break the circuit.

切勿将伏特表串联接入电路。它的电阻极大，实际上会断开电路。
Remember that in a uniform field, voltage decreases linearly in the direction of the field.

记住在匀强电场中，电压沿电场方向线性减小。
Use correct units: volt (V), not voltmeter reading in “amps”.

使用正确单位：伏特（V），不要把伏特表读数说成“安培”。
In internal resistance graphs, label the intercepts clearly and include uncertainties.

在内阻实验中，标清截距并包含不确定度分析。

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Voltage: Physical Meaning and Measurement | 电压的物理意义与测量