BISTABILITY AND FLUCTUATIONS FOR AN INCANDESCENT LIGHT-BULB

We develop a simple kinetic model to explain the hysteresis that occur s when an incandescent light bulb is controlled by a rheostat in the e xternal circuit. The model is based on changes in the temperature of t he filament that are associated with internal energy changes due to ra diation and Joule heating. The radiative processes are idealized as oc curring via photons lost and gained by a blackbody, while the dynamics of the electric current are treated via the Langevin equation. Quantu m corrections to the elementary process description of blackbody radia tion are derived. Like the ballast resistor, the model exhibits hyster esis due to a region of bistability of the temperature as a function o f the resistance in the rheostat, the criterion for stability being th at the temperature of the filament decreases with increasing resistanc e in the rheostat, Explicitly including variations in the current, we show that temperature and current fluctuations are correlated and that they diverge as the thresholds for stability are approached. It may b e possible to study these divergences experimentally.