Kelvin Water Dropper
Lord Kelvin’s water dropper (1867) generates thousands of volts from nothing but dripping water and a feedback loop. A tiny random charge imbalance is amplified because each inductor ring charges the opposite collector’s drops — positive feedback from cross-coupling. Watch the voltage grow exponentially until sparks fly.
dQ/dt ∝ Q ⇒ Q(t) = Q0 · eλt (exponential growth from positive feedback)
How it works
Two streams of water drops fall from a reservoir through two metal rings (inductors) into two metal cans (collectors) below. The key trick is the cross-coupling: the left inductor ring is electrically connected to the right collector, and vice versa. When a tiny random charge appears on one collector, it influences the inductor on the opposite side, which charges the drops falling through it. Those charged drops land in their collector, increasing its charge — which in turn influences the other inductor even more strongly. The result is exponential growth.
The feedback loop
Suppose the right collector is slightly positive. Because it is connected to the left inductor, the left inductor is also positive. By electrostatic induction, drops falling through the left inductor acquire negative charge (positive charge is repelled up the stream, negative stays on the drop). These negatively-charged drops land in the left collector, making it more negative. The left collector is connected to the right inductor, so the right inductor becomes negative, inducing positive charge on drops falling through it. Those land in the right collector, making it more positive. Each half of the cycle amplifies the other.
Sparking
The voltage keeps growing until the electric field between the two collectors exceeds the dielectric breakdown of air (about 30 kV/cm at atmospheric pressure, but practical Kelvin water droppers spark at a few thousand volts due to the larger gap). At that point, a spark jumps between the collectors, partially discharging them. The process then begins again from the reduced charge.
Historical significance
William Thomson (Lord Kelvin) invented this device in 1867. It is remarkable because it generates high voltage from no initial power source — just gravity and water. The initial charge asymmetry comes from random thermal fluctuations. It is one of the simplest demonstrations of positive feedback in physics, and a beautiful example of how symmetry breaking (tiny initial noise) plus amplification (cross-coupling) produces dramatic macroscopic effects.