Which device serves to govern the electric power delivered to the apparatus it is connected to?

The device that serves to govern the electric power delivered to the apparatus it is connected to is a controller. Controllers are designed to manage and regulate the flow of electrical energy, thereby ensuring that the connected equipment operates under the desired conditions, such as speed, pressure, temperature, or position. They can adjust power levels based on feedback from the system they are managing, making them essential for optimizing performance and protecting equipment from overloads or undesired operational conditions.

While other devices like transformers, switches, and relays play crucial roles in electrical systems, they do not specifically function to govern the electric power in the controlling sense. A transformer alters voltage levels without controlling power delivery in a dynamic manner. A switch simply connects or disconnects electrical circuits and does not manage power flow. A relay acts as an electrical switch but is a component that responds to control signals rather than being a governing device itself. Therefore, the controller's specific purpose of regulating and adjusting power makes it the correct answer to the question.