This project demonstrates the classic half-wave rectifier. The transformer isn't necessary; it's just there as an example of a typical half-wave rectifier circuit. Two things to note: 1.) the recitifier diode causes a voltage drop (a.k.a. "diode drop") of ~0.7V 2.) the 2nd circuit includes a capacitor that charges up to near the peak voltage and stays there unless the load draws a lot of current in which case the discharge during each cycle is noticeable compared to the charge each cycle.