Kirchoff Laws

Two fundamental circuit laws governing current and voltage in any electrical network.

Kirchoff’s Current Law (KCL): the sum of currents entering a node equals the sum leaving.

∑Iin=∑Iout\sum{I_{in}}=\sum{I_{out}}

where:

  • Σ Iin = currents entering the node (A)
  • Σ Iₒᵤₜ = currents leaving the node (A)

We can show this applied to three battery cells arranged in parallel with a load:

Kirchoff's Current Law applied to cells in parallel

Kirchoff’s Voltage Law (KVL): the sum of voltages around any closed loop equals zero.

∑V=0\sum{V}=0

Showing this applied to three battery cells arranged in series with a load:

Kirchoff's voltage law applied to three cells in series

Both directly govern parallel cell groups and series strings (KCL for parallel, KVL for series).

See also: Ohm’s Law, Watt Hour