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Varistors are known to use for over-voltage protection, as they have high electrical resistance at low voltage which decreases as the voltage is raised.(wikipedia).

But is there any electrical component or simple solution to function reversely?! In contrast, A non-linear resistor to have low electrical resistance at low voltage and high resistance at high voltage? or simpler closed-circuit when no voltage, and open-circuit when voltage greater than any constant applied?

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    \$\begingroup\$ A fuse would work ... maybe with a resistor in series. \$\endgroup\$ – brhans Feb 23 '17 at 12:10
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    \$\begingroup\$ Sounds like an XY problem. Try explaining what you are trying to do such as (I suspect) protecting a circuit from a certain level of over-voltage? \$\endgroup\$ – Andy aka Feb 23 '17 at 13:05
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A positive temperature coefficient (PTC) thermistor, though it won't reach open circuit.

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  • \$\begingroup\$ Interesting suggest. if I see correctly, it seems the idea here is PTC heats in high voltage conditions because of ohmic loss and then rises its resistance. so it seems to be a side effect. could you explain it more in this particular application, such as variables to consider and ... \$\endgroup\$ – 2i3r Feb 23 '17 at 17:11
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A light bulb would have that characteristic, but with a thermal delay. Sometimes the difference between cold and hot can be 10:1.

But a more appropriate solution might be (since we're just guessing at what you're trying to do) a current sink. The current sink might sink 1ma at 1V and 1mA at 60V. So the effective resistance changes from 1K to 60K. Simple current sinks can be made with op-amps and transistors or just transistors depending on what rails are available and how stable the current should be.

You can even just use a JFET or depletion-mode MOSFET with the gate tied to the source.

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