Loopon

Meet Loopon, a battery who sends charge around a circuit and gets every volt back.

Kirchhoff's voltage law says that if you go all the way around any closed loop in a circuit, adding the voltage rises and subtracting the voltage drops, the total is zero. Gustav Kirchhoff published this rule, together with his current rule, in 1845.

It is conservation of energy for charge. A battery gives each coulomb some energy, and the components around the loop take it all back before the charge returns to where it started.

Take a 9 V battery connected to two resistors in series, one of 2 kΩ and one of 1 kΩ. The current is 9 / 3000 = 3 mA, so the drops are 3 mA × 2 kΩ = 6 V and 3 mA × 1 kΩ = 3 V. The rise of 9 V and the drops of 6 V and 3 V add to zero.

Engineers use this law, with the current law at junctions, to work out the currents in complicated circuits, writing one equation per loop and solving them together.