📚 IGCSE Physics: Current and Voltage Relationships in Circuits | IGCSE物理：电路中的电流与电压关系
This article explains how electric current and voltage behave in circuits, covering Ohm’s law, the current-voltage (I-V) characteristics of different components, and the key rules for series and parallel circuits. These ideas are central to the Edexcel IGCSE Physics course and appear in both Paper 1 and Paper 2.
本文讲解电路中电流与电压的行为，涵盖欧姆定律、不同元件的电流-电压（I-V）特性，以及串联和并联电路的关键规律。这些内容是 Edexcel IGCSE 物理课程的核心，在 Paper 1 和 Paper 2 中都会出现。
1. What is Electric Current? | 什么是电流？
Electric current is the rate of flow of electric charge. In metal wires, the moving charges are free electrons. Although each electron drifts slowly, the electric field set up by the battery pushes the whole chain of electrons around the circuit very quickly.
电流是电荷流动的速率。在金属导线中，运动的电荷是自由电子。虽然每个电子漂移得很慢，但电池建立的电场会很快推动电路中整条“电子链”定向运动。
The size of the current is the amount of charge passing a point per second. The unit of current is the ampere (A). One ampere means one coulomb of charge passes a point every second.
电流的大小等于每秒通过某一点的电荷量。电流的单位是安培（A）。1 安培表示每秒通过某一点的电荷量为 1 库仑。
I = Q ÷ t
In this equation, I is current in amperes (A), Q is charge in coulombs (C), and t is time in seconds (s).
在这个公式中，I 是电流，单位为安培（A）；Q 是电荷量，单位为库仑（C）；t 是时间，单位为秒（s）。
The conventional direction of current is from the positive terminal of the battery to the negative terminal. This is opposite to the direction in which electrons actually flow.
习惯规定的电流方向是从电池正极流向负极，这与电子实际运动的方向相反。
2. What is Voltage (Potential Difference)? | 什么是电压（电势差）？
Voltage, also called potential difference (p.d.), is the energy transferred to or from each unit of charge as it moves between two points in a circuit. A battery supplies energy to the charge; a component transfers energy away from the charge.
电压，也叫电势差，是电荷在电路中两点之间移动时，每单位电荷获得或失去的能量。电池给电荷提供能量；电阻等元件则把能量从电荷转移出去。
The unit of voltage is the volt (V). One volt is equal to one joule of energy transferred per coulomb of charge.
电压的单位是伏特（V）。1 伏特等于每库仑电荷转移 1 焦耳的能量。
V = W ÷ Q
Here, V is voltage in volts (V), W is energy in joules (J), and Q is charge in coulombs (C).
其中，V 是电压，单位为伏特（V）；W 是能量，单位为焦耳（J）；Q 是电荷量，单位为库仑（C）。
A voltmeter is always connected in parallel with a component to measure the potential difference across it.
伏特计（电压表）必须与被测元件并联，用来测量该元件两端的电势差。
3. How Voltage Drives Current | 电压如何推动电流
Think of voltage as the “push” that moves charge around the circuit. Without a potential difference, no charge will flow and there is no current.
可以把电压理解为推动电荷在电路中运动的“推力”。如果没有电势差，电荷就不会定向移动，也就没有电流。
A battery creates a potential difference by transferring chemical energy to the charge. The charge then flows around the circuit, giving energy to components such as lamps, resistors, and motors.
电池通过把化学能转移给电荷来产生电势差。电荷在电路中流动，并把能量传递给灯泡、电阻、电动机等元件。
For a fixed resistance, increasing the voltage increases the current. Doubling the voltage doubles the current if the resistance stays constant.
对于固定电阻，增大电压会增大电流。如果电阻保持不变，电压加倍时电流也加倍。
This relationship between current and voltage is the foundation of electric circuit analysis in IGCSE Physics.
电流与电压之间的这种关系，是 IGCSE 物理中电路分析的基础。
4. Ohm’s Law and Resistance | 欧姆定律与电阻
Resistance is a measure of how much a component opposes the flow of charge. The resistance of a component is defined as the ratio of voltage across it to the current through it.
电阻是衡量元件阻碍电荷流动程度的物理量。某个元件的电阻定义为它两端电压与通过电流的比值。
R = V ÷ I
Resistance is measured in ohms (Ω). One ohm is the resistance of a component when one volt across it causes a current of one ampere.
电阻的单位是欧姆（Ω）。1 欧姆表示元件两端加 1 伏特电压时，流过 1 安培的电流。
Ohm’s law states that, for a metallic conductor at constant temperature, the current through it is directly proportional to the voltage across it.
欧姆定律指出：对于温度保持不变的金属导体，流过导体的电流与导体两端的电压成正比。
V = I × R
This equation is used constantly in circuit calculations. Rearranged, it gives I = V ÷ R or R = V ÷ I.
这个公式在电路计算中经常使用。变形后可得到 I = V ÷ R 或 R = V ÷ I。
Not all components obey Ohm’s law. A component that does not obey Ohm’s law is called a non-ohmic conductor, such as a filament lamp or a diode.
并非所有元件都遵守欧姆定律。不遵守欧姆定律的元件称为非欧姆导体，例如白炽灯丝和二极管。
5. The I-V Characteristics of a Resistor | 电阻器的 I-V 特性
An I-V characteristic graph shows how the current through a component changes as the voltage across it changes. For a fixed resistor at constant temperature, the graph is a straight line through the origin.
I-V 特性曲线表示通过元件的电流随其两端电压的变化。对于温度保持不变的定值电阻，图像是一条通过原点的直线。
Because the graph is straight and passes through the origin, the current is directly proportional to the voltage. The gradient of the graph is 1 ÷ R.
由于图像是过原点的直线，说明电流与电压成正比。图像的斜率等于 1 ÷ R。
If you reverse the voltage, the current also reverses direction, but the graph remains a straight line through the origin. This shows that the resistor behaves the same for current flowing in either direction.
如果电压反向，电流也反向，但图像仍然是通过原点的直线。这说明电阻对正反两个方向的电流表现相同。
In a circuit experiment, you vary the voltage using a variable resistor or a power supply, and measure the current with an ammeter.
在电路实验中，可用滑动变阻器或可调电源改变电压，并用安培计测量电流。
| Voltage / V | 0 | 1 | 2 | 3 | 4 |
| Current / A | 0 | 0.20 | 0.40 | 0.60 | 0.80 |
In this example, the resistance is 5 Ω for every reading, so the component obeys Ohm’s law.
在这个例子中，每次测量的电阻都是 5 Ω，因此该元件遵守欧姆定律。
6. The I-V Characteristics of a Filament Lamp | 灯丝的 I-V 特性
A filament lamp contains a thin metal wire that becomes hot and glows when current flows. As the current increases, the temperature of the filament increases.
白炽灯内有一根细金属丝，电流通过时会发热并发光。电流增大时，灯丝的温度会升高。
When the temperature of the metal filament rises, the metal ions vibrate more. They collide more often with the free electrons, so the resistance of the filament increases.
当金属灯丝温度升高时，金属离子振动加剧，与自由电子的碰撞更加频繁，因此灯丝的电阻增大。
The I-V graph for a filament lamp is therefore a curve, not a straight line. The curve bends away from the voltage axis at higher voltages.
因此，灯丝的 I-V 图像是曲线而不是直线。在电压较高时，曲线偏离电压轴。
At first, a small increase in voltage produces a relatively large current. As the voltage continues to rise, the same increase in voltage produces a smaller current because resistance has increased.
起初，小幅增加电压会产生较大的电流。随着电压继续升高，同样增加电压所产生的电流变小，因为电阻已经增大。
The filament lamp is a non-ohmic conductor, even though it is made of metal, because its temperature is changing continuously.
灯丝虽然是金属制成，但由于温度不断变化，它属于非欧姆导体。
This is why the I-V graph is not a straight line through the origin.
这就是它的 I-V 图像不是过原点的直线的原因。
7. The I-V Characteristics of a Diode | 二极管的 I-V 特性
A diode is a component that lets current flow in one direction only. The arrow in the circuit symbol shows the direction in which current can flow.
二极管是一种只允许电流沿一个方向流动的元件。电路符号中的箭头表示电流允许流过的方向。
When the diode is connected in forward bias, a small voltage is needed before a significant current starts to flow. For a typical silicon diode, this threshold is about 0.7 V.
当二极管正向偏置时，需要很小的电压才会产生明显的电流。对于典型的硅二极管，这个门槛电压约为 0.7 V。
When the diode is connected in reverse bias, it blocks current almost completely. Only a tiny leakage current may flow, often close to zero.
当二极管反向偏置时，它几乎完全阻断电流，最多只有极小的漏电流，通常接近于零。
The I-V graph of a diode is therefore highly asymmetrical: nearly flat in reverse bias, and very steep after the threshold voltage in forward bias.
因此，二极管的 I-V 图像非常不对称：反向偏置时图像近乎水平，正向偏置超过门槛电压后图像非常陡峭。
A light-emitting diode (LED) emits light when current flows through it in the forward direction. LEDs are used in indicator lamps and display screens.
发光二极管（LED）在正向电流流过时会发光。LED 常用于指示灯和显示屏中。
Diodes and LEDs must not be connected directly across a battery without a resistor, or the current could become large enough to damage them.
二极管和 LED 不能没有限流电阻就直接接到电池两端，否则电流过大会损坏元件。
8. Series Circuits: What Stays Constant? | 串联电路：什么保持不变？
In a series circuit, components are connected end to end, forming a single path for current. There is only one route, so the same current flows through every component.
在串联电路中，元件首尾相连，形成一条单一的电流路径。由于只有一条通路，流过每个元件的电流都相同。
This is an important rule: in a series circuit, the current is the same at every point.
这是一个重要规律：在串联电路中，电流处处相等。
I₁ = I₂ = I₃
The total voltage of the supply is equal to the sum of the voltages across each component. Energy is conserved because each component uses part of the total energy supplied.
电源总电压等于各元件两端电压之和。这是因为能量守恒，每个元件都消耗了电源提供的部分能量。
V_total = V₁ + V₂ + V₃
In a series circuit, resistances add together. The total resistance is the sum of all the individual resistances.
在串联电路中，电阻相加。总电阻等于各个电阻之和。
R_total = R₁ + R₂ + R₃
If one component in a series circuit fails and the circuit breaks, current stops everywhere. This is why old-style fairy lights often went out completely when one bulb failed.
如果串联电路中某个元件断开，整个电路都会断路，电流处处停止。这就是老式彩灯中一个灯泡烧坏会导致整串灯全灭的原因。
9. Parallel Circuits: How Voltage and Current Split? | 并联电路：电压与电流如何分配？
In a parallel circuit, components are connected across the same two points. This provides more than one path for current to flow.
在并联电路中，元件连接在相同的两点之间，为电流提供了多条路径。
The voltage across each branch of a parallel circuit is the same. Every component connected directly across the supply receives the full supply voltage.
并联电路中各支路两端的电压相等。直接跨接在电源两端的每个元件都获得完整的电源电压。
V_supply = V₁ = V₂ = V₃
The total current from the supply is the sum of the currents in all the branches.
电源提供的总电流等于各支路电流之和。
I_total = I₁ + I₂ + I₃
Adding more branches in parallel reduces the total resistance of the circuit. This is because more paths make it easier for charge to flow.
并联电路中增加支路会减小总电阻。这是因为路径越多，电荷流动越容易。
For two resistors in parallel, the total resistance can be found using the following equation.
对于两个并联电阻，可用下面的公式求总电阻。
R_total = (R₁ × R₂) ÷ (R₁ + R₂)
For example, if R₁ = 4 Ω and R₂ = 6 Ω, then R_total = (4 × 6) ÷ (4 + 6) = 24 ÷ 10 = 2.4 Ω.
例如，若 R₁ = 4 Ω，R₂ = 6 Ω，则 R_total = (4 × 6) ÷ (4 + 6) = 24 ÷ 10 = 2.4 Ω。
The total resistance in parallel is always smaller than the smallest individual resistance. This is a common exam question.
并联电路的总电阻总是小于其中最小的那个电阻。这是一道常见考题。
10. Using an Ammeter and Voltmeter | 安培计与伏特计的使用
An ammeter measures the current flowing through a circuit. It must be connected in series with the component so that all the charge flowing through the component also flows through the meter.
安培计（电流表）测量流过电路的电流。它必须与元件串联，使流过元件的所有电荷也全部流过电流表。
An ideal ammeter has zero resistance, so it does not reduce the current. In practice, a good ammeter has very low resistance.
理想安培计电阻为零，因此不会减小电流。实际中，好的安培计电阻非常小。
A voltmeter measures the potential difference across a component. It must be connected in parallel with the component.
伏特计（电压表）测量元件两端的电势差。它必须与元件并联。
An ideal voltmeter has infinite resistance, so almost no current flows through it. In practice, a good voltmeter has very high resistance.
理想伏特计电阻无穷大，因此几乎没有电流流过它。实际中，好的伏特计电阻非常高。
A common mistake is connecting an ammeter in parallel or a voltmeter in series. This is dangerous and gives wrong readings.
常见的错误是让安培计并联或让伏特计串联。这样既危险又会使读数不准。
Remember: Ammeter in series, Ammeter in series, Ammeter in series. And Voltmeter in parallel.
请记住：安培计串联，安培计串联，安培计串联。伏特计并联。
11. Investigating Current and Voltage: Practical Skills | 探究电流与电压：实验技能
To investigate the relationship between current and voltage, set up a circuit with a battery, a fixed resistor, an ammeter in series, and a voltmeter in parallel with the resistor.
要探究电流与电压的关系，可搭建一个电路，包含电池、定值电阻、串联的安培计，以及与电阻并联的伏特计。
Use a variable resistor (rheostat) or a variable power supply to change the voltage across the resistor. Record the ammeter and voltmeter readings for at least six different voltage settings.
使用滑动变阻器或可调电源来改变电阻两端的电压。至少记录六组不同电压下的安培计和伏特计读数。
Plot a graph of current on the y-axis against voltage on the x-axis. If the graph is a straight line through the origin, the resistor is obeying Ohm’s law.
以纵轴为电流、横轴为电压作图。如果图像是通过原点的直线，说明该电阻遵守欧姆定律。
When testing a filament lamp, the temperature changes as the current changes. You must switch off the circuit between readings and allow the lamp to cool, so that the results are more consistent.
测试灯丝时，电流变化会引起温度变化。每次读数之间应断开电路，让灯丝冷却，这样结果会更稳定。
When testing a diode, use a protective resistor in series to prevent the current from exceeding the diode’s maximum rating.
测试二极管时，要串联一个保护电阻，防止电流超过二极管的最大允许值。
Always record units in your data table. Check zero errors on the meters before starting.
记录数据时一定要写单位。开始实验前还应检查电表是否有零位误差。
12. Summary and Exam Tips | 总结与考试提示
At constant temperature, the current through a metallic conductor is directly proportional to the voltage across it. This is Ohm’s law.
在温度不变时，通过金属导体的电流与其两端电压成正比。这就是欧姆定律。
For series circuits: current is the same everywhere, voltages add, and resistances add. For parallel circuits: voltage is the same everywhere, currents add, and total resistance is smaller than the smallest branch resistance.
串联电路：电流处处相等，电压相加，电阻相加。并联电路：电压处处相等，电流相加，总电阻小于最小支路电阻。
The I-V graph of a fixed resistor is a straight line through the origin. The I-V graph of a filament lamp bends because resistance increases with temperature. The I-V graph of a diode is one-way and asymmetric.
定值电阻的 I-V 图像是过原点的直线。灯丝的 I-V 图像弯曲，因为温度升高使电阻增大。二极管的 I-V 图像是单向且不对称的。
- Always state units: volts (V), amperes (A), ohms (Ω).
- Always connect ammeters in series and voltmeters in parallel.
- Remember that Ohm’s law only applies to ohmic conductors at constant temperature.
- Read exam questions carefully: does the graph ask for I against V or V against I?
- 一定要写单位：伏特（V）、安培（A）、欧姆（Ω）。
- 安培计一定串联，伏特计一定并联。
- 记住欧姆定律只适用于温度不变的欧姆导体。
- 仔细读题：题目要求画 I-V 图还是 V-I 图？
Practising circuit calculations and sketching I-V graphs will help you gain full marks in this topic.
多加练习电路计算和 I-V 图像作图，能帮助你在这一知识点上获得满分。
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