Visible light emitting diodes (LEDs) have been widely used as power indicators. However, after the power is switched off, it takes a while for the LED to go off. Many students were fascinated by this simple demonstration. In this paper, by making use of computer-based data acquisition and modeling, we show the voltage across the LED undergoing an exponential decay after the power is switched off. We also describe a new approach for determining Planck's constant using LEDs. The simple experiment can be used either in an interactive lecture demonstration or an entry-level physics lab.