Current & Voltage in Circuits | 电路中的电流与电压

📚 Current & Voltage in Circuits | 电路中的电流与电压

Electric circuits are the foundation of all modern technology. Understanding how current and voltage behave in different circuit arrangements is essential for IGCSE Physics. This guide covers the key concepts, laws, and experimental skills you need for the Edexcel exam.

电路是现代一切技术的基础。理解电流和电压在不同电路连接方式中的行为，是 IGCSE 物理的核心内容。本指南涵盖 Edexcel 考试所需的关键概念、定律和实验技能。

1. Electric Current | 电流

Electric current is the rate of flow of electric charge. In metal wires, the charge is carried by free electrons. The unit of current is the ampere (A), and current is measured using an ammeter connected in series with the component.

电流是电荷流动的速率。在金属导线中，电荷由自由电子携带。电流的单位是安培（A），测量电流需要使用串联在电路中的安培表。

Current can be calculated using the equation:

Q = I × t

where Q is charge in coulombs (C), I is current in amperes (A), and t is time in seconds (s). Charges of the same sign repel each other, so charge flows from a region of higher potential energy to lower potential energy along a conductor.

其中 Q 是电荷量，单位为库仑（C）；I 是电流，单位为安培（A）；t 是时间，单位为秒（s）。同种电荷相互排斥，因此电荷会沿导体从电势能较高的区域流向电势能较低的区域。

For example, a current of 2 A flowing for 10 s transfers a charge of 20 C. When solving problems, always check that the time is converted to seconds where necessary.

例如，2 A 的电流流动 10 秒，转移的电荷量为 20 C。解题时务必检查时间是否已换算为秒。

2. Voltage (Potential Difference) | 电压（电势差）

Voltage, or potential difference, is the energy transferred per unit charge as charge moves between two points in a circuit. The unit is the volt (V), equal to one joule per coulomb. A voltmeter is used to measure potential difference and is always connected in parallel with the component.

电压，又称电势差，是电荷在电路中两点之间移动时，每单位电荷所转移的能量。单位是伏特（V），1 伏特等于 1 焦耳每库仑。电压用伏特表测量，测量时必须与元件并联。

The key relationship is:

V = W / Q

where W is the electrical energy transferred in joules (J), Q is charge in coulombs (C), and V is potential difference in volts (V). A battery supplies electrical energy to the circuit; components such as lamps and resistors transfer this energy to light and heat.

其中 W 是转移的电能（焦耳，J），Q 是电荷量（库仑，C），V 是电势差（伏特，V）。电池为电路提供电能，而灯泡、电阻等元件则将电能转化为光能和热能。

A common error is confusing voltage with current. Voltage is the “push” that drives charge around the circuit, while current is the actual flow of charge. The same voltage can produce different currents depending on the resistance.

常见错误是混淆电压与电流。电压是推动电荷在电路中移动的“驱动力”，而电流是电荷的实际流动。相同的电压在不同电阻下会产生不同的电流。

3. Resistance & Ohm’s Law | 电阻与欧姆定律

Resistance is a measure of how difficult it is for charge to flow through a component. The unit of resistance is the ohm (Ω). Components with higher resistance allow less current for the same voltage.

电阻是衡量电荷通过元件难易程度的物理量，单位是欧姆（Ω）。在相同电压下，电阻越大的元件允许通过的电流越小。

Ohm’s law states that the current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature and other physical conditions remain constant. This gives:

欧姆定律指出：在温度和其他物理条件保持恒定时，通过金属导体的电流与其两端电势差成正比。由此得到：

V = I × R

where V is potential difference in volts, I is current in amperes, and R is resistance in ohms.

其中 V 是电势差（伏特），I 是电流（安培），R 是电阻（欧姆）。

Ohm’s law only applies to ohmic conductors, such as fixed resistors at constant temperature. Non-ohmic components, like filament lamps and diodes, do not follow this simple proportionality.

欧姆定律仅适用于恒定温度下的线性导体，例如固定电阻。非欧姆元件如白炽灯丝和二极管，不遵循这种简单的正比关系。

4. Circuit Symbols & Diagrams | 电路符号与电路图

Standard symbols are used in circuit diagrams so that any scientist can understand them. For the Edexcel exam, you must be able to recognise and draw the following symbols: cell, battery, switch, lamp, fixed resistor, variable resistor, ammeter, voltmeter, diode, thermistor and LDR.

电路图使用标准符号，以便所有科学家都能理解。在 Edexcel 考试中，你必须能识别和绘制以下符号：电池、电池组、开关、灯泡、固定电阻、可变电阻、安培表、伏特表、二极管、热敏电阻和光敏电阻。

An ammeter is placed in series to measure the current through a branch.
A voltmeter is placed in parallel to measure the potential difference across a component.

安培表串联在支路中以测量电流。
伏特表并联在元件两端以测量电势差。

A variable resistor allows the resistance to be changed, which controls the current in the circuit. A diode only allows current to flow in one direction, acting as a one-way valve for charge.

可变电阻允许改变电阻值，从而控制电路中的电流。二极管只允许电流沿一个方向流动，如同电荷的单向阀。

When drawing circuit diagrams, use a pencil and ruler for straight wires, and make sure the circuit forms a complete loop for current to flow.

绘制电路图时，用铅笔和直尺画直线导线，并确保电路形成完整的回路，电流才能流动。

5. Series Circuits | 串联电路

In a series circuit, components are connected one after another along a single path. If one component breaks, the circuit is broken and no current can flow.

在串联电路中，元件沿着单一路径一个接一个地连接。若某个元件断开，整个电路断开，电流停止流动。

In a series circuit, the current is the same at all points. Because there is only one path, charge cannot be created or destroyed, and the rate of flow is identical everywhere.

在串联电路中，各点的电流处处相同。因为只有一条路径，电荷不能被创造或消灭，所以任何位置的流动速率都相同。

The total potential difference supplied by the battery is shared between the components according to their resistances:

电池提供的总电势差会根据各元件的电阻大小分配在元件之间：

V_total = V₁ + V₂ + V₃ + …

The total resistance of resistors in series is the sum of the individual resistances:

串联电阻的总电阻等于各电阻之和：

R_total = R₁ + R₂ + R₃ + …

For example, two resistors of 4 Ω and 6 Ω in series give a total resistance of 10 Ω. If connected to a 6 V battery, the current is 6 V ÷ 10 Ω = 0.6 A.

例如，两个 4 Ω 和 6 Ω 的电阻串联，总电阻为 10 Ω。若连接到 6 V 电池，电流为 6 V ÷ 10 Ω = 0.6 A。

6. Parallel Circuits | 并联电路

In a parallel circuit, components are connected on separate branches. Each branch provides an independent path for current, so if one branch breaks, the others continue to work.

在并联电路中，元件连接在不同的支路上。每条支路为电流提供独立路径，因此若某条支路断开，其他支路仍能正常工作。

The potential difference across each branch is the same and equals the battery voltage:

并联电路中，每条支路两端的电势差相同，且等于电池电压：

V_branch = V_battery

The total current from the battery splits between the branches. The sum of the currents in each branch equals the total current supplied:

电池输出的总电流在支路之间分配。各支路电流之和等于总电流：

I_total = I₁ + I₂ + I₃ + …

Adding more resistors in parallel always decreases the total resistance. This is because there are more paths for the charge to flow through. For two equal resistors R in parallel, the total resistance is R/2.

并联的连接电阻越多，总电阻反而越小。这是因为电荷有更多路径可以通过。两个阻值均为 R 的电阻并联，总电阻为 R/2。

The total resistance for resistors in parallel is calculated using:

并联电阻的总电阻计算公式为：

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …

Household wiring is connected in parallel. This ensures that each appliance receives the same 230 V supply and can be switched on or off independently.

家庭电路采用并联连接。这样可以确保每个用电器都获得相同的 230 V 电压，并且可以独立开关。

7. I-V Characteristics | 电流-电压特性曲线

Investigating the I-V (current-potential difference) characteristic of a component is a core practical for Edexcel IGCSE. The circuit consists of a cell, an ammeter in series, a voltmeter in parallel, a variable resistor to change the voltage, and the component under test.

测量元件的 I-V（电流-电势差）特性曲线是 Edexcel IGCSE 的核心实验。电路包括电池、串联的安培表、并联的伏特表、用于改变电压的可变电阻以及待测元件。

For a fixed resistor at constant temperature, the I-V graph is a straight line through the origin, showing that current is proportional to voltage. The resistor obeys Ohm’s law.

对于恒定温度下的固定电阻，I-V 图像是一条过原点的直线，说明电流与电压成正比。该电阻遵循欧姆定律。

For a filament lamp, the I-V graph curves upwards as voltage increases. As the lamp gets hotter, the metal filament’s resistance increases, so the current rises less and less steeply. The graph is symmetrical for forward and reverse voltages.

对于白炽灯，I-V 图像随电压增大而向上弯曲。灯丝温度升高，金属电阻增大，所以电流上升的斜率逐渐减缓。图像在正向和反向电压下对称。

For a diode, current flows freely in the forward direction but is almost zero in the reverse direction. The graph is a steep curve in the forward quadrant and nearly flat along the axis in the reverse quadrant. A diode has a small threshold voltage, typically about 0.6 V for silicon.

对于二极管，正向电流容易通过，反向电流几乎为零。图像在正向象限为陡峭曲线，在反向象限几乎贴着横轴。二极管存在较小的阈值电压，硅二极管通常约为 0.6 V。

8. Factors Affecting Resistance | 影响电阻的因素

Several factors affect the resistance of a conductor. Length directly increases resistance: a longer wire forces charge to pass through more atoms, causing more collisions. If the length is doubled, the resistance is doubled.

导体电阻受多种因素影响。长度直接增加电阻：导线越长，电荷需要碰撞更多原子，阻力越大。长度加倍，电阻也加倍。

Cross-sectional area decreases resistance: a thicker wire provides more lanes for charge to flow. For a conductor of uniform cross-section, resistance is inversely proportional to area.

横截面积减小电阻：导线越粗，为电荷提供更多通道。对于截面均匀的导体，电阻与面积成反比。

Material type matters: copper has low resistance and is used for wiring, while nichrome has high resistance and is used in heating elements.

材料类型也很重要：铜电阻低，用于导线；镍铬合金电阻高，用于发热元件。

Temperature affects resistance: for metals, resistance increases with temperature because lattice vibrations are greater, causing more electron collisions. For thermistors, resistance decreases as temperature rises, making them useful in temperature sensors.

温度影响电阻：金属的电阻随温度升高而增大，因为晶格振动加剧，电子碰撞更频繁。热敏电阻则相反，温度升高时电阻降低，因此常用于温度传感器。

9. Worked Example | 例题解析

Example: A 12 V battery is connected to a 3 Ω resistor and a 6 Ω resistor in series.

例题：一个 12 V 电池与一个 3 Ω 和一个 6 Ω 的电阻串联连接。

Step 1 – Calculate the total resistance: R_total = 3 + 6 = 9 Ω

步骤 1 – 计算总电阻：R_total = 3 + 6 = 9 Ω

Step 2 – Calculate the current using Ohm’s law: I = V / R = 12 / 9 = 1.33 A

步骤 2 – 用欧姆定律计算电流：I = V / R = 12 / 9 = 1.33 A

Step 3 – Calculate the voltage across the 3 Ω resistor: V₃ = I × R = 1.33 × 3 = 4.0 V

步骤 3 – 计算 3 Ω 电阻两端的电压：V₃ = I × R = 1.33 × 3 = 4.0 V

Step 4 – Calculate the voltage across the 6 Ω resistor: V₆ = I × R = 1.33 × 6 = 8.0 V

步骤 4 – 计算 6 Ω 电阻两端的电压：V₆ = I × R = 1.33 × 6 = 8.0 V

Check: 4.0 V + 8.0 V = 12 V, as expected from Kirchhoff’s voltage law. The larger resistance gets a proportionally larger share of the voltage.

检验：4.0 V + 8.0 V = 12 V，符合基尔霍夫电压定律。电阻越大，分到的电压越高。

10. Common Mistakes & Exam Tips | 常见错误与考试提示

One common mistake is connecting a voltmeter in series or an ammeter in parallel. Always remember: ammeter in series, voltmeter in parallel. Reversing them can damage the instruments and gives meaningless readings.

常见错误之一是把伏特表串联，或把安培表并联。请记住：安培表串联，伏特表并联。连接错误可能损坏仪器，且读数没有意义。

Another mistake is misapplying Ohm’s law to non-ohmic components. The equation V = I × R still defines resistance at a point, but the ratio V/I is not constant for a lamp or diode. You cannot use the gradient of a curved I-V graph directly to find resistance; you must read off V and I at the chosen point.

另一个错误是对非欧姆元件误用欧姆定律。公式 V = I × R 仍可定义某点处的电阻，但灯泡和二极管的 V/I 比值不恒定。不能直接用弯曲 I-V 图像的斜率求电阻，必须在所选点读出具体的 V 和 I。

Always convert units carefully. Milliamperes (mA) must be converted to amperes by dividing by 1000, and kilohms (kΩ) to ohms by multiplying by 1000. For example, 25 mA = 0.025 A, and 4.7 kΩ = 4700 Ω.

务必注意单位换算。毫安（mA）除以 1000 换算为安培，千欧（kΩ）乘以 1000 换算为欧姆。例如，25 mA = 0.025 A，4.7 kΩ = 4700 Ω。

In exam questions about series circuits, remember that current is the same everywhere, so find the total resistance first and then the current. For parallel circuits, find the voltage first because it is the same across each branch.

在串联电路考题中，记住电流处处相同，所以先求总电阻再求电流。在并联电路考题中，先找电压，因为各支路电压相同。

Finally, be able to describe the I-V experiment carefully: vary the potential difference using a variable resistor, record both ammeter and voltmeter readings, and plot a graph of current on the y-axis against potential difference on the x-axis.

最后，要能清楚描述 I-V 实验过程：用可变电阻改变电势差，同时记录安培表和伏特表读数，并以电流为纵轴、电势差为横轴绘制图像。

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Current & Voltage in Circuits | 电路中的电流与电压