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"Paradoxical behaviour of mechanical and electrical networks" [1] states that adding a current-carrying path can increase the voltage drop across a circuit. What is the simplest example of a circuit (preferably consisting solely of two-terminal devices) that exhibits such behavior?

[1] Cohen, Joel E., and Paul Horowitz. "Paradoxical behaviour of mechanical and electrical networks." Nature 352.6337 (1991): 699-701.
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  • $\begingroup$ You might want to try a Wheatstone bridge type of circuit with two non-linear elements. $\endgroup$
    – Johannes
    Dec 8, 2012 at 7:29
  • $\begingroup$ @Johannes what kind of non-linear elements are you talking about? $\endgroup$ Dec 9, 2012 at 6:13
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    $\begingroup$ Have a look at this paper: rockefeller.edu/labheads/cohenje/PDFs/… $\endgroup$
    – Johannes
    Dec 9, 2012 at 12:57
  • $\begingroup$ thanks, exactly what I was looking for! I was wondering whether it was possible to construct such a circuit using only (ohmic) resistors, but I guess it's not possible. $\endgroup$ Dec 10, 2012 at 10:49
  • $\begingroup$ Indeed, it’s impossible using only ohmic resistors; this result is called Rayleigh’s monotonicity theorem. $\endgroup$
    – knzhou
    Apr 5, 2022 at 3:18

1 Answer 1

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Here is a simple circuit that demonstrates Braess's Paradox. If the red switch is open, 1.5 Amps will flow from the power source to the ground. If the red switch is closed, ADDING A CONDUCTOR to the circuit, the current DROPS to 1.0 Amp.

A simple circuit that demonstrates Braess's Paradox.

When the switch is closed, no current flows through the Zener diodes.

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    $\begingroup$ Nice example, and welcome to Phys.SE! $\endgroup$
    – knzhou
    Apr 5, 2022 at 3:17

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