Physics · Circuits

Kirchhoff Loop and Junction Rules

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Equivalent ResistanceReduce the same network

Key takeaway

At a split node, charge does not pile up: the incoming current equals the outgoing branch currents, so the live parallel case obeys I_total = I_2 + I_3.
Around a closed loop, choose one walking direction and sign convention; the battery rise and resistor drops then add to zero.

Common misconception

Kirchhoff's rules are separate formulas you memorize after the circuit already makes sense.

The rules are conservation statements for the same live circuit you can already see: current does not disappear at a node, and energy per charge does not appear from nowhere around a closed loop.

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Reference and support

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Equation snapshotJunction rule · Current split at the grouped nodeShow 2 equations

Junction rule
$\sum I_{in} = \sum I_{out}$
Charge does not disappear at a node, so incoming current must match outgoing current.
Current split at the grouped node
$I_{total} = I_{2} + I_{3}$
In the parallel grouped case, the source current splits into the two branch currents and recombines later.

Why it behaves this way

Explanation

Kirchhoff's rules are conservation habits for reading one real circuit. At a junction, charge cannot pile up, so the incoming current must match the outgoing currents. Around a closed loop, each battery rise is spent by resistor drops, so the signed voltage changes add to zero.

This module keeps the setting small: one outer resistor and one highlighted two-resistor group. In the parallel case, that group creates one visible split node and two branch loops. In the series case, the split disappears and the same current crosses every resistor. That is enough to practice current balance, loop balance, and sign convention without turning the page into a general circuit solver.

Key ideas

01At a split node, charge does not pile up: the incoming current equals the outgoing branch currents, so the live parallel case obeys I_total = I_2 + I_3.

02Around a closed loop, choose one walking direction and sign convention; the battery rise and resistor drops then add to zero.

03Kirchhoff's rules do not replace Ohm's law. They work with V = IR to turn the same live currents and drops into solvable equations.

Worked examples

Live Kirchhoff checks

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the exact grouped circuit on screen. First read the split-node currents, then trace one loop with a single sign convention so the numbers and equations stay connected.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current grouped circuit, what current-balance equation does the active node obey, and what current passes through R3?

V

Battery voltage

12 V

R_{2}

Grouped resistor 2

6 ohm

R_{3}

Grouped resistor 3

12 ohm

1. Start from the live path structure

The highlighted group is parallel right now, so one source current reaches the split node and becomes two branch currents.

2. Write the current-balance equation

I_{total} = I_{2} + I_{3}

3. Substitute the live current values

1.5 = 1 + 0.5

4. Read or solve the R3 branch current

That leaves

I_{3} = 0.5

Junction balance

I_{total} = I_{2} + I_{3}, I_{3} = 0.5

At the split node, the total current is being conserved by becoming the two branch currents. The larger-resistance branch keeps the smaller current.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows one battery on the left, one outer resistor R1 on the top path, and a highlighted two-resistor group on the right. The group can appear either as two parallel branches with a real split node or as one series path with no split node.

Overlays can show current arrows, voltage labels, a node guide, a loop guide, and the reduction cue. The readout card and graphs update from the same grouped circuit.

Graph summary

The current graph shows total current together with the R2 and R3 branch currents as R3 changes. The voltage-share graph shows the R1 drop, the grouped-block drop, and the live R3 drop for the same sweep. Use them as response summaries of the same grouped circuit rather than as a second model.

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