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Kirchhoff's Laws

Kirchhoff's current law says the sum of currents into a node equals the sum out, because charge is conserved. Kirchhoff's voltage law says the sum of voltages around any closed loop is zero. Together with Ohm's law, these two laws are enough to solve any DC circuit.

\sum I_{in} = \sum I_{out}

current law (KCL) at a node

\sum U = 0

voltage law (KVL) around a loop

Symbols

$I$	current into/out of the node	A
$U$	voltage drop around the loop	V

Example

At a node, $5$ A and $3$ A flow in, and $I$ A flows out:

$5+3=I \Rightarrow I=8$ A.

Pick a sign convention for current direction and voltage drop once, and stick to it throughout the circuit.

Practise direct current for free →

← Series and Parallel · Capacitor →

Part of Electric Circuits: Direct current.