Physical proof of the occurrence of the Braess Paradox in electrical circuits

The Braess Paradox is the counterintuitive phenomenon that can occur in a user-optimized network system, such as a transportation network, where adding an additional link to the network increases the cost (travel time) for every user. In electrical circuits, electrons, analogous to drivers in a transportation network, traverse the network so that no electron can unilaterally change its cost (voltage drop) from an origin to a destination. In this paper, we show that the Braess Paradox can occur in electrical circuits consisting of diodes and resistors. We report measurements confirming the occurrence of the Braess Paradox in two different circuits, one with highly nonlinear link cost functions ($I\text{-}V$ characteristics). These measurements show that the voltage increases, rather than decreases, when a link is added to the circuit under constant demand (current). This discovery identifies novel circuits in which the voltage and current can be independently adjusted. It also yields insights into the Braess Paradox and transportation networks through a new computational mechanism