Final answer:
An autotransformer uses a single coil for both primary and secondary functions, inducing a voltage across portions of the same winding by Faraday's law of induction, as described in the provided figures and text.
Step-by-step explanation:
A transformer that uses only one coil for both the primary and secondary functions is known as an autotransformer. Unlike a conventional transformer, which has two separate coils (primary and secondary) wound around a ferromagnetic core to transfer energy, the autotransformer uses a single, continuous winding that acts as both the primary and the secondary. This type of transformer capitalizes on Faraday's law of induction, as detailed in the provided text and figures like 23.27 and 20.31, to induce a voltage across portions of the same winding. With an AC input voltage, a time-varying magnetic flux passes through the winding, inducing an AC output voltage. An autotransformer can be more efficient and economical in some applications; however, it does not provide the same isolation between circuits as a two-coil transformer.