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Assume that we have a circuit that is connected with components that have positive resistance. At this point the effective resistance between every two node is positive. (below is an example of such circuit)

schematic

simulate this circuit – Schematic created using CircuitLab

Now, if we add components with negative resistance, we can have negative effective resistance between two nodes. (Here the effective resistance between node 1 and node 3, has become -2).

schematic

simulate this circuit At this point, is it possible to make the effective resistance between every two nodes positive by adding more negative resistance components?

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  • \$\begingroup\$ "negative" resistance is not a real world phenomenon to my knowledge... \$\endgroup\$
    – vicatcu
    Commented Jun 17, 2016 at 21:05
  • \$\begingroup\$ negative resistance does exist, see tunneling diodes, and it got Esaki a Nobel prize. it's relative to operating conditions. the posters question is not really clear \$\endgroup\$
    – b degnan
    Commented Jun 17, 2016 at 21:20
  • \$\begingroup\$ @vicatcu Even if you think it doesn't exist, think of it as an abstract element. @ b degnan, where is the ambiguity? \$\endgroup\$
    – user114313
    Commented Jun 17, 2016 at 21:31
  • \$\begingroup\$ Please make this question clearer, potentially with a pseudo-circuit diagram. You can use the circuit diagram tool in the editor, and remember to use text labels liberally to refer to node points etc \$\endgroup\$
    – Daniel
    Commented Jun 17, 2016 at 22:27
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    \$\begingroup\$ Of course, negative resistances do exist - and are widely used in practice (filters, oscillators). There are various realization methods - but always on the basis of active componenets (transistors, opamps). Negative resistances are nothing else than voltage controlled current sources with the current going through the controlling voltage source. \$\endgroup\$
    – LvW
    Commented Jun 18, 2016 at 8:11

1 Answer 1

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It is possible to have a loop with a mixture of positive and negative resistance, provided that the overall sum is positive or negative. In either case, in the absence of an external current source or sink, the voltage at all points in the loop will be equal, which will in turn imply that the current must be zero. If there were a loop where the sum of positive and negative resistances totaled zero, then it would be possible for an arbitrary amount of current to flow around the loop, creating potential differences at nodes around the loop.

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  • \$\begingroup\$ here my question is not about current and voltage (yes they have equal voltage here). My question is with a circuit in which equivalent resistance between some nodes are negative, can we plug some negative resistance between nodes in order to have positive "equivalent resistance" between all nodes? \$\endgroup\$
    – user114313
    Commented Jun 17, 2016 at 23:30
  • \$\begingroup\$ @user114313: If you can add negative resistance components in series with positive ones, you can reduce the positive resistance. If positive and negative resistances with different magnitudes are in parallel, the sign of the result will be that of the smaller resistance. \$\endgroup\$
    – supercat
    Commented Jun 18, 2016 at 0:45
  • \$\begingroup\$ @supercat: You're right that if the total resistance is strictly positive and there are no non-proportional sources (a negative resistance is a proportional dependent source), the current will converge to zero. But for strictly negative total resistance this will not happen. Sure, it is the only solution to the system, but it isn't a stable equilibrium -- any noise disturbing the system will produce positive feedback in the dependent sources and current will "run away" until limited by some non-linear effect. \$\endgroup\$
    – Ben Voigt
    Commented Jun 18, 2016 at 15:20
  • \$\begingroup\$ @BenVoigt: Good catch, and one I should have recognized, since IR-compensation systems that are compensated to negative net resistance end up behaving that way. \$\endgroup\$
    – supercat
    Commented Jun 18, 2016 at 15:50
  • \$\begingroup\$ @BenVoigt: Thinking about it a little more, in the absence of any inductance or capacitance in the loop, could any non-equilibrium condition be created by externally-attached devices in a way that would persist when they were disconnected? A positive resistance loop will be stable even in the presence of inductance or capacitance, while any non-zero capacitance or inductance will facilitate a runaway condition, but I can't think of any way to set up the runaway condition in ideal negative resistors by temporarily connecting external stimuli. Is that possible? \$\endgroup\$
    – supercat
    Commented Jun 18, 2016 at 15:58

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