Kirchhoff's Loop Rule · 基尔霍夫回路定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| Kirchhoff's loop rule/ˈkɜːkhɒfs luːp ruːl/ | 基尔霍夫回路定则 | jī ěr huò fū huí lù dìng zé |
Walk a full loop and you return to the same energy
- Follow one charge all the way around a circuit loop.
- It gains energy at the battery and loses it at each resistor.
- Back at the start, its energy is exactly what it began with.
- That simple bookkeeping is the loop rule — a tool for any circuit.
走完一整圈,你回到相同的能量
- 跟着一个电荷绕电路回路走一整圈。
- 它在电池处获得能量,在每个电阻处失去能量。
- 回到起点时,它的能量正好是它开始时的。
- 那个简单的记账就是回路定律——任何电路的工具。
The loop rule: voltages sum to zero
- Around any closed loop, the voltage changes add to zero: $\sum V = 0$.
- Every rise (battery) is matched by the drops (resistors).
- For a single loop: $\varepsilon - IR_1 - IR_2 = 0$.
- It is really energy conservation, counted per unit charge.
回路定律:电压之和为零
- 绕任何闭合回路,电压变化加起来为零:$\sum V = 0$。
- 每一次上升(电池)都由下降(电阻)相抵。
- 对单个回路:$\varepsilon - IR_1 - IR_2 = 0$。
- 它其实是能量守恒,按单位电荷来计。
Kirchhoff's loop rule states that around any closed loop: · 基尔霍夫回路定律指出，围绕任何闭合回路：
$\sum V = 0$ around a loop — energy conservation per charge. · $\sum V = 0$ 围绕回路 —— 每单位电荷的能量守恒。
A $12\ \text{V}$ battery drives current through a $2\ \Omega$ and a $2\ \Omega$ resistor in series. Find $I$ (in A). · 一个$12\ \text{V}$电池驱动电流通过一个$2\ \Omega$和一个$2\ \Omega$电阻串联。求$I$（单位为A）。
$12 - I(2) - I(2) = 0 \Rightarrow 12 = 4I \Rightarrow I = 3\ \text{A}$.
Getting the signs right
- Going through a battery from $-$ to $+$ is a rise ($+\varepsilon$).
- Crossing a resistor with the current is a drop ($-IR$).
- Cross it against the current and it counts as a rise ($+IR$).
- Pick a direction, walk the loop, and keep the signs consistent.
把符号弄对
- 从 $-$ 到 $+$ 穿过电池是一次上升($+\varepsilon$)。
- 顺着电流穿过电阻是一次下降($-IR$)。
- 逆着电流穿过它则算作上升($+IR$)。
- 选一个方向,绕回路走,保持符号一致。
Crossing a resistor in the direction of the current is a voltage drop ($-IR$). · 顺着电流方向穿过电阻是电压降落（$-IR$）。
With the current, a resistor drops the potential by $IR$. · 顺电流方向，电阻使电势降低$IR$。
Select all · 所有 true statements about the loop rule. · 选择关于回路定律的所有正确陈述。
Loop rule: ΣV = 0, energy conservation, consistent signs. Currents-sum-to-zero is the junction rule. · 回路定律：ΣV = 0，能量守恒，符号一致。电流之和为零是节点定律。
Why it must be true
- A charge returning to its start is at the same potential.
- So the total potential change around the loop is zero.
- Energy given by the source equals energy taken by the components.
- No loop can create or destroy energy for the charge.
为什么它必然成立
- 回到起点的电荷处于相同的电势。
- 所以绕回路的总电势变化为零。
- 电源给出的能量等于元件取走的能量。
- 没有回路能为电荷创造或消灭能量。
Kirchhoff's loop rule · 基尔霍夫回路定律
Around any closed loop the voltage rises equal the voltage drops. Sort each crossing. · 围绕任何闭合回路，电压升高等于电压降落。对每次穿越进行分类。
The loop rule is a statement of the conservation of: · 回路定律是以下哪项守恒的表述：
A charge returns to the same potential — energy is conserved. · 电荷回到同一电位 —— 能量守恒。
Using it to solve circuits
- Write one loop equation for each independent loop.
- Combine with the junction rule to get enough equations.
- Solve them together for the unknown currents.
- Complex networks fall to a handful of linear equations.
用它解电路
- 为每个独立回路写一个回路方程。
- 与节点定律结合,得到足够的方程。
- 一起解出未知电流。
- 复杂网络归结为少数几个线性方程。
The loop rule is combined with the ____ rule to solve multi-loop circuits. · 回路定律与____定律结合用于求解多回路电路。
The junction rule provides the extra current equations. · 节点定律提供了额外的电流方程。
A $9\ \text{V}$ battery drives one current through a $2\ \Omega$ and a $1\ \Omega$ resistor in series.
- Loop rule: $9 - I(2) - I(1) = 0$.
- So $9 = 3I$, giving $I = 3\ \text{A}$.
一个 $9\ \text{V}$ 电池驱动单一电流通过串联的 $2\ \Omega$ 和 $1\ \Omega$ 电阻。
- 回路定律:$9 - I(2) - I(1) = 0$。
- 所以 $9 = 3I$,得 $I = 3\ \text{A}$。
Keep your sign convention consistent. Decide a loop direction first, then a resistor crossed with the current is $-IR$ and against it is $+IR$. Flipping signs midway is the usual source of wrong answers.
保持你的符号约定一致。先定一个回路方向,然后顺着电流穿过的电阻是 $-IR$,逆着的是 $+IR$。中途翻转符号是错误答案的常见来源。
Kirchhoff's loop rule 基尔霍夫回路定则 says the voltage changes around any closed loop sum to zero: $\sum V = 0$. It is energy conservation per charge — a battery rise balances the resistor drops. Track signs carefully and pair it with the junction rule.
基尔霍夫回路定律说绕任何闭合回路的电压变化之和为零:$\sum V = 0$。它是单位电荷的能量守恒——电池的上升与电阻的下降相抵。仔细追踪符号,并与节点定律配对。