Kirchhoff's Junction Rule
| English | Chinese | Pinyin |
|---|---|---|
| junction | 节点 | jié diǎn |
| Kirchhoff's junction rule | 基尔霍夫节点定则 | jī ěr huò fū jié diǎn dìng zé |
At a fork in the wire, where does the current go?
- Wires often split: one path becomes two or three.
- The current can't pile up or vanish at the split.
- Whatever flows in must flow out — that is the junction rule.
- It is the partner of the loop rule for solving networks.
The junction rule: current in = current out
- At any junction 节点 (a meeting of wires), $\sum I_{\text{in}} = \sum I_{\text{out}}$.
- Charge is conserved, so none builds up at the point.
- If $I_1$ enters and $I_2, I_3$ leave: $I_1 = I_2 + I_3$.
- The branches share the incoming current between them.
Split the current
Wire two parallel branches and see the current divide between them at the junction.
Kirchhoff's junction rule states that at a junction:
$\sum I_{\text{in}} = \sum I_{\text{out}}$ — charge is conserved.
$7\ \text{A}$ enters a junction and one branch carries $4\ \text{A}$. Find the other branch current (in A).
$7 = 4 + I_2 \Rightarrow I_2 = 3\ \text{A}$.
A point where wires meet and current can split is called a ____.
That meeting point is a junction (or node).
Why: charge can't accumulate
- A junction is just a point of wire — it holds no charge.
- So the rate in must equal the rate out at every instant.
- This is the conservation of charge applied to a point.
- Break it and charge would build up without limit — impossible.
The junction rule expresses the conservation of:
No charge accumulates at a point — charge is conserved.
Bigger branches carry more current
- At equal voltage, the branch with less resistance carries more current.
- Current splits in inverse proportion to the branch resistances.
- The easiest path takes the biggest share.
- Add up all the branch currents and you recover the total.
At a split, the branch with less resistance carries more current.
At equal voltage, current is largest in the lowest-resistance branch.
Select all true statements about the junction rule.
Junction rule: current in = out, charge conservation, more current in easy branches. Voltage-round-a-loop is the loop rule.
Solving with both rules
- Junction rule gives current equations; loop rule gives voltage equations.
- Together they give enough equations for every unknown current.
- Label each branch current, apply both rules, and solve.
- This pair cracks any resistor network, however tangled.
A $5\ \text{A}$ current reaches a junction and splits into two branches; one carries $2\ \text{A}$.
- Junction rule: $5 = 2 + I_2$.
- So the other branch carries $I_2 = 3\ \text{A}$.
The junction rule is about current (charge conservation), while the loop rule is about voltage (energy conservation). Don't mix them up: currents meet at junctions, voltages balance around loops.
Kirchhoff's junction rule 基尔霍夫节点定则 says the current into a junction equals the current out: $\sum I_{\text{in}} = \sum I_{\text{out}}$. It is conservation of charge at a point. Paired with the loop rule, it solves any resistor network.