Kirchhoff's Voltage Law (KVL)

Formula

Description

Kirchhoff's Voltage Law states that the algebraic sum of all voltages around any closed loop in a circuit must equal zero. This is a consequence of the conservation of energy: a charge traveling around a closed loop must return to its starting potential. Voltage sources are positive (energy added) and voltage drops across resistors and other components are negative (energy consumed). KVL is one of the two fundamental laws (along with KCL) used in systematic circuit analysis methods like mesh analysis and loop analysis.

Variables

• V₁, V₂, V₃... — Voltages around the loop (V), with sign convention: positive for rises, negative for drops

Practical Notes

Enter all voltage rises as positive values and all voltage drops as negative values. The result should be zero (or very close) for a valid circuit loop. A non-zero sum indicates a measurement error or a missing voltage source/drop in the analysis. KVL applies to any closed path, not just physical component loops.