At a junction in a circuit, three wires meet. Wire A carries 5A flowing INTO the junction. Wire B carries 2A flowing INTO the junction. Current in Wire C is unknown.
What is the current in Wire C?
7A flows OUT through Wire C! Kirchhoff’s junction rule is simply conservation of charge: current in = current out. With 5A and 2A both flowing into the junction, 7A must flow out. Charge cannot pile up at the junction — electrons don’t accumulate or vanish. Every ampere that arrives must leave.
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Build a circuit with multiple junctions and loops. Watch the current split and recombine at each node. Click any junction to see Kirchhoff’s junction rule verified: total current in always equals total current out. Trace a loop to see the voltage drops sum to zero.
ΣI_in = ΣI_out | ΣV_loop = 0
Junction rule = charge conservation. Loop rule = energy conservation. Two fundamental laws give you the power to solve any circuit.
Your house’s circuit breaker panel is one big junction. The current entering from the power line splits across every circuit in your home. If all the branch currents don’t add up — there’s a dangerous fault.
Neurons in your brain obey Kirchhoff’s rules too! Ion currents flowing into a neural junction must equal currents flowing out — the biophysics of thought follows circuit laws.
Every electronic device is designed using software (SPICE) that applies Kirchhoff’s rules to thousands of nodes simultaneously. Your phone’s chip was validated by solving millions of junction and loop equations.
City water systems follow the same math! Flow in = flow out at every junction, and pressure drops around any loop sum to zero. Kirchhoff’s rules apply to any conserved flow network.
“Kirchhoff’s two rules are conservation of charge and conservation of energy wearing circuit disguises. Master them, and no circuit is unsolvable.”
Circuit Analyzer
Build multi-loop circuits with batteries, resistors, and junctions. The analyzer automatically applies Kirchhoff’s rules to find every current and voltage. Watch current flow through the circuit, verify the junction rule at each node, and trace loops to see the voltage sum to zero.
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Start with a simple two-resistor series circuit — the loop rule is just V = IR₁ + IR₂. Now add a parallel branch and watch current split at the junction. Build a Wheatstone bridge (four resistors in a diamond) and find the balance condition where no current flows through the middle wire. Challenge: add two batteries facing opposite directions and predict which way current flows before the simulation reveals it.
Kirchhoff’s rules transform circuit analysis from guesswork into algebra. At every junction, charge is conserved. Around every loop, energy is conserved. These two principles — applied systematically — can solve any circuit ever built.