Resistor Combinations: Series, Parallel and Mixed Circuits | 电阻组合：串联、并联与混联电路

📚 Resistor Combinations: Series, Parallel and Mixed Circuits | 电阻组合：串联、并联与混联电路

In CIE A-Level Physics, resistor combinations appear in both Paper 1 multiple-choice questions and Paper 2/3 structured problems. Understanding series and parallel rules is essential for analysing current, potential difference and power in a wide range of circuits, including potential dividers and circuits with internal resistance.

在 CIE A-Level 物理中，电阻组合是试卷 1 选择题和试卷 2/3 结构题中的常见考点。掌握串联和并联的规律，对于分析各种电路中的电流、电势差和功率至关重要，包括电位分压器和含内阻的电路。

1. Why Resistor Combinations Matter | 为什么电阻组合如此重要

Real circuits rarely contain a single resistor. Resistors are combined to control current, divide voltage or share power safely. Identifying whether resistors are in series, parallel or a mixed arrangement is the first step in circuit analysis.

实际电路中很少只有一个电阻。电阻被组合使用，以控制电流、分配电压或安全地分担功率。判断电阻是串联、并联还是混联，是电路分析的第一步。

In CIE exams, you may be asked to calculate the total resistance between two terminals, or to explain why adding resistors in parallel lowers the total resistance. You must also be able to redraw circuits to make the arrangement clearer.

在 CIE 考试中，你可能需要计算两个接线端之间的总电阻，或解释为什么并联电阻会使总电阻降低。你还必须能够重画电路，使连接关系更清晰。

• Series resistors share the same current.
• Parallel resistors share the same potential difference.

• 串联电阻中的电流相同。
• 并联电阻两端的电势差相同。

2. Series Resistors: Same Current, Shared Voltage | 串联电阻：电流相同，电压分配

When resistors are connected end to end, there is only one path for charge carriers, so the current I is the same through each resistor. The total potential difference across the combination equals the sum of the individual potential differences.

当电阻首尾相连时，电荷载体只有一条通路，因此通过每个电阻的电流 I 相同。组合两端的总电势差等于各电阻两端电势差之和。

Using V = IR for each resistor gives Vₜ = IR₁ + IR₂ + IR₃. Since the current is common, the effective series resistance Rₛ is:

利用 V = IR 对每个电阻列式，可得 Vₜ = IR₁ + IR₂ + IR₃。因为电流相同，等效串联电阻 Rₛ 为：

Rₛ = R₁ + R₂ + R₃ + …

This rule is easy to apply but several students forget that the largest resistor in series dissipates the most power because P = I²R and I is the same for all.

这个规律很容易应用，但一些学生忘记：串联中阻值最大的电阻耗散功率最大，因为 P = I²R，而各电阻电流 I 相同。

3. Parallel Resistors: Same Voltage, Shared Current | 并联电阻：电压相同，电流分配

When resistors are connected side by side between two junctions, each resistor has the same potential difference V across it. The total current from the source splits between the branches, and the sum of branch currents equals the source current.

当电阻并排连接在两个节点之间时，每个电阻两端的电势差 V 相同。从电源流出的总电流在各支路之间分配，各支路电流之和等于电源电流。

For two resistors in parallel, the individual currents are I₁ = V/R₁ and I₂ = V/R₂. The total current is Iₜ = V/R₁ + V/R₂, so the reciprocal effective resistance Rₚ satisfies:

对于两个并联电阻，各支路电流为 I₁ = V/R₁ 和 I₂ = V/R₂。总电流为 Iₜ = V/R₁ + V/R₂，因此等效电阻的倒数 Rₚ 满足：

1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃ + …

For two parallel

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