We derive a model for voltage-induced wetting, so-called electrowetting, from the principle of virtual displacement. Our model includes the possibility that charge is trapped in or on the wetted surface. Experimentally, we show reversible electrowetting for an aqueous droplet on an insulating layer of 10 mu m thickness. The insulator is coated with a highly fluorinated layer impregnated with oil, providing a contact-angle hysteresis lower than 2 degrees. Analyzing the data with our model, we find that until a threshold voltage of 240 V, the induced charge remains in the liquid and is not trapped. For potentials beyond the threshold, the wetting force and the contact angle saturate, in line with the occurrence of trapping of charge in or on the insulating layer. The data are independent of the polarity of the applied electric field and of the ion type and molarity. We suggest possible microscopic origins for charge trapping.