Which electrical law states that the algebraic sum of voltages around a closed loop is zero?

Kirchhoff’s voltage law states that the algebraic sum of voltages around a closed electrical loop is zero.

The law follows from conservation of energy. A charge moving around a complete circuit can gain energy from sources such as batteries and lose energy in components such as resistors, but its net energy change after returning to the starting point must be zero.

Gustav Kirchhoff published his circuit laws in 1845. Engineers use the voltage law to analyze series circuits and more complicated networks containing multiple loops. Each voltage rise and drop is assigned a sign according to the chosen direction around the loop.

Kirchhoff’s voltage law is distinct from Kirchhoff’s current law. The voltage law applies to closed loops, whereas the current law concerns a junction and follows conservation of electric charge. Real circuits also require careful attention to component polarity and measurement conventions.