Kirchhoff's Junction Rule
Introduced| English |
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| Kirchhoff's junction rule/ˈkɜːkhɒfs ˈdʒʌŋkʃn ruːl/ |
A river splits — but not a drop is lost
- A river reaches a fork and splits into two streams; add the two flows and you get the original.
- At a wire junction, current splits the same way — and none of it vanishes.
- Whatever charge flows in must flow out — charge is never created or lost.
- This is Kirchhoff's junction rule 基尔霍夫节点定律, the partner of the loop rule.
The junction rule
- At any junction (a point where wires meet), the current in equals the current out.
- In symbols: $\sum I_{\text{in}} = \sum I_{\text{out}}$.
- It is really conservation of charge — charge can't pile up at a point.
- So if $I_1$ flows in and splits into $I_2$ and $I_3$, then $I_1 = I_2 + I_3$.
$5\ \text{A}$ reaches a junction and splits into two branches; one carries $2\ \text{A}$. What does the other carry, in $\text{A}$?
$5 = 2 + I \Rightarrow I = 3\ \text{A}$.
Kirchhoff's junction rule is a statement of the conservation of:
Charge can't pile up at a point, so current in equals current out.
At a junction, the current in equals the current ____.
$\sum I_{\text{in}} = \sum I_{\text{out}}$.
How current splits in parallel
- At the start of a parallel section, the total current divides among the branches.
- More current takes the path of lower resistance (the easier route).
- At the far end, the branch currents rejoin and add back to the total.
- The junction rule keeps the books balanced at every split and merge.
At a split into parallel branches, more current flows through the branch with:
Current favours the easier path — the branch of lower resistance.
Select all true statements about the junction rule.
The junction rule conserves charge: current divides and rejoins, never used up.
Solving with both rules together
- The junction rule gives equations about currents; the loop rule gives equations about voltages.
- Together they turn any DC circuit into a set of equations you can solve.
- Write junction equations at the nodes, loop equations around the loops, and solve.
- These two rules are all you need for even the most tangled resistor network.
Kirchhoff's junction rule
Charge cannot pile up at a junction. Sort each current as flowing in or out.
Current is used up as it passes through a junction.
Current divides but is never used up — what flows out equals what flows in.
The junction rule is about charge, not energy (that's the loop rule). Current does not get "used up" at a junction — it only divides. The amounts flowing out must add up exactly to the amount flowing in.
A current of $5\ \text{A}$ reaches a junction and splits into two branches. One branch carries $2\ \text{A}$. What does the other carry?
- Junction rule: $5 = 2 + I \Rightarrow I = 3\ \text{A}$.
The two branch currents ($2\ \text{A}$ and $3\ \text{A}$) add back to the $5\ \text{A}$ that came in.
Kirchhoff's junction rule: at any junction, current in equals current out ($\sum I_{\text{in}} = \sum I_{\text{out}}$) — conservation of charge. Current divides at a split (favouring lower resistance) and rejoins later. With the loop rule, it solves any DC circuit.