Energy Conservation in a Motor-Driven Generator

An electric motor converts electrical energy into mechanical work and an electric generator converts mechanical work into electrical energy. The symmetry between the motor and generator naturally leads to questions about creating a perpetual motion machine. The allure of this question has inspired textbook problems, physics education articles, and award-winning physics demonstrations. It is commonly taught that spinning a generator faster produces a larger electromotive force (EMF), because the generator’s instantaneous EMF is proportional to the angular rate of rotation. When making this point in class, students will often ask about an interesting thought experiment, which is depicted in Fig. 1. The student question is as follows: “If an electric motor is connected via a system of gears to an electric generator, so that the generator spins faster than the motor, then does the generator’s output power P_G exceed the motor’s input power P_M ?”