📚 Kirchhoff's Second Law | 基尔霍夫第二定律
Kirchhoff's second law, also known as the voltage law (KVL), is a fundamental principle for analysing electrical circuits. It states that around any closed loop in a circuit, the algebraic sum of all potential differences (voltages) is zero. This law is a consequence of energy conservation: as a charge travels around a loop, the total energy gained from sources such as batteries must equal the total energy lost in resistances and other components.
基尔霍夫第二定律，也称为电压定律（KVL），是分析电路的基本原理。它表明，在电路中环绕任何一个闭合回路，所有电势差（电压）的代数和为零。这条定律是能量守恒的结果：当电荷绕回路移动时，从电池等源获得的总能量必须等于在电阻及其他元件中损耗的总能量。
1. Statement of the Law | 定律的表述
ΣIR. Equivalently, if we assign a sign to each potential difference (rise or drop) as we traverse the loop, the total sum is ΣV = 0. The loop may be traced in either direction, but the chosen direction must be maintained consistently for all components in that loop.
对于网络中的任何一个闭合回路，我们可以写出电动势（emf）之和等于电流与电阻乘积之和：Σε = ΣIR。等效地，如果我们在绕回路行走时给每个电势差（升高或降低）规定符号，则总和为 ΣV = 0。回路可以沿任一方向绕行，但一旦选定方向，回路中所有元件的符号必须一致确定。
ul when the loop contains identifiable voltage sources and resistive components. It emphasises that the total energy supplied per unit charge is entirely dissipated as heat in resistive parts of the circuit.
形式 Σε = ΣIR 在回路包含可识别的电压源和阻性元件时特别有用。它强调了单位电荷所获得的总能量全部以热形式耗散在电路的电阻部分。
2. Conservation of Energy | 能量守恒
f electric potential energy. As it moves through resistors, it loses energy at a rate proportional to the current and resistance; the energy dissipated per coulomb is the potential drop V = IR. Around a closed loop, the initial and final potentials are identical, so net energy change is zero.
KVL 是能量守恒在电学形式上的直接表达。当一库仑电荷通过电动势为 ε 的电池时，它获得 ε 焦耳的电势能。当它经过电阻时，以与电流和电阻成比例的速率损失能量；每库仑耗散的能量即电势降落 V = IR。绕闭合回路一周后，起点与终点的电势相同，因此净能量变化为零。
This is why the sum of all emfs (energy rises per unit charge) must equal the sum of all potential drops (energy falls per unit charge) around any complete loop. Any apparent violation would imply a perpetual energy source or sink, which is impossible under normal circuit conditions.
这就是为什么环绕任何完整回路的全部电动势（单位电荷的能量升高）之和必须等于全部电势降落（单位电荷的能量降低）之和。任何表面上的违反都意味着存在永动能源或能量消失，这在正常电路条件下是不可能的。
3. Sign Conventions for Potential Differences | 电势差的符号规定
To apply the law correctly, a sign convention is essential. First, choose a direction to traverse the loop (clockwise is often convenient). Consider each component: when moving through a cell from its negative terminal to its positive terminal, this is a potential rise and is taken as positive (+ε). Moving from positive to negative gives a potential drop and is taken as negative (−ε).
要正确应用该定律，符号规定十分关键。首先，选定绕行回路的方向（顺时针通常较为方便）。逐一考虑每个元件：当沿回路从电池的负端走向正端时，这是一次电势升高，取为正（+ε）。从正端走向负端时为电势降落，取为负（−ε）。
For a resistor, if the traversing direction is the same as the assumed current direction, the potential drops; we record −IR. If the traversing direction is opposite to the assumed current, the potential rises; we record +IR. Consistency in these sign assignments ensures that the algebraic sum correctly reflects energy changes.
对于电阻，如果绕行方向与假定的电流方向相同，则电势降落，记为 −IR。如果绕行方向与假定的电流方向相反，则电势升高，记为 +IR。符号分配的一致性确保代数和正确反映能量变化。
Summary table of conventions:
符号规定总结表：
| Component | Traversal relative to component | Sign in ΣV |
|---|---|---|
| Battery (emf ε) | From − to + | +ε |
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