Studying the electromagnetic compatibility of an Unmanned Aerial Vehicle (UAV) using full-wave electromagnetic simulations is computationally challenging. A UAV can exhibit unintentional coupling from far-field sources as well as from sources in its close vicinity. For example, in many applications, the UAV carries a payload that consists of a transmitting antenna to communicate/characterize receivers on the ground. Therefore, there is a strong need for an accurate and rapid technique to quantify RF coupling to the UAV subcomponents due to a wide range of incident electromagnetic radiation. In this work, we study RF coupling to a quadcopter UAV in a computationally efficient manner using the Equivalent Circuit Approach (ECA). The ECA is based on modeling the direct coupling to the wiring system with a Thevenin equivalent circuit terminated with the load under test. We study different circuit representations for this Thevenin equivalent circuit and show the advantages of each representation. Moreover, the equivalent circuit of the UAV wires is used to study different linear/nonlinear loads in a fraction of the time required by full-wave simulations. In addition, we show how the ECA provides physical insight that can facilitate the prediction of RF coupling to a UAV and other complex systems.