📚 Kirchhoff's First Law | 基尔霍夫第一定律
Kirchhoff's first law, often called the junction rule or Kirchhoff's current law (KCL), is a cornerstone of circuit analysis in A-Level Physics. It states that at any electrical junction, the total current entering the junction equals the total current leaving the junction. This law allows us to analyse complex circuits where currents split or combine, and it follows directly from the principle of conservation of electric charge.
基尔霍夫第一定律通常称为节点定则或基尔霍夫电流定律（KCL），是 A-Level 物理电路分析的基础。它指出：在任何电路节点处，流入该节点的总电流等于流出该节点的总电流。这一定律使我们能够分析电流分岔或汇合的复杂电路，并且它直接源自电荷守恒原理。
1. Statement of the Law | 定律表述
For any junction in an electrical circuit, the algebraic sum of all currents is zero. Equivalently, the sum of currents flowing into the junction equals the sum of currents flowing out of the junction. If we label currents entering as positive and currents leaving as negative, then:
对于电路中的任意节点，所有电流的代数和为零。等价地，流入节点的电流之和等于流出节点的电流之和。如果我们把流入的电流标记为正、流出的电流标记为负，则有：
∑I = 0 at a junction
In the more intuitive form, it is written as:
在更直观的形式中，它可写作：
∑Iin = ∑Iout
Here, I represents electric current measured in amperes (A). The terms "in" and "out" refer to the chosen reference directions of current at the junction. This statement is valid for steady currents and also for time-varying currents at any instant, because charge cannot accumulate at a junction.
这里 I 表示以安培（A）为单位的电流。"流入"和"流出"指在节点处选定的电流参考方向。该表述对恒定电流成立，对时变电流在任一瞬态也成立，因为电荷不能在节点处积累。
2. Charge Conservation Basis | 电荷守恒基础
Kirchhoff's first law is not an independent experimental law; it is a direct consequence of charge conservation. Electric current is the rate of flow of charge, so if more charge entered a junction per second than left it, charge would build up at that point. In practice, junctions in conducting materials do not store significant charge, so the net charge entering per unit time must be zero.
基尔霍夫第一定律并不是一条独立的实验定律；它是电荷守恒的直接结果。电流是电荷流动的速率，因此如果每秒流入节点的电荷多于流出的电荷，电荷就会在该点积累。实际上，导电材料中的节点不会储存大量电荷，所以单位时间内净流入的电荷必须为零。
Mathematically, for a junction with n branches, we can write:
数学上，对于有 n 条支路的节点，我们可以写：
I₁ + I₂ + ... + Iₙ = 0
where the sign of each current depends on whether it is entering or leaving the junction. The underlying principle is that the total charge in an isolated system remains constant; a junction in a circuit is a point, not a reservoir of charge.
其中每一项电流的符号取决于它是流入还是流出节点。其根本原理是孤立系统的总电荷保持不变；电路中的节点是一个点，而不是电荷的储存库。
3. Defining Current Direction | 定义电流方向
In circuit analysis, current direction is assigned conventionally as the direction of positive charge flow, even though in metallic conductors the actual charge carriers are electrons moving in the opposite direction. Before applying Kirchhoff's first law, you must mark a reference direction for each branch current. The law then gives the relationship among these currents.
在电路分析中，电流方向按惯例规定为正电荷流动的方向，尽管在金属导体中实际的载流子是沿相反方向运动的电子。在应用基尔霍夫第一定律之前，你必须为每条支路电流标出一个参考方向。然后该定律给出这些电流之间的关系。
For example, consider a junction where three wires meet. If currents I₁ and I₂ are shown entering the junction and I₃ is shown leaving, then the law gives:
例如，考虑三条导线交汇的节点。如果 I₁ 和 I₂ 被标为流入节点，I₃ 被标为流出，那么定律给出：
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