A memristor is a type of resistor in which the flow of electrical current in an electronic circuit is determined by the amount of charge that has previously flowed through it.
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Together, capacitors, inductors and resistors form the three basic circuit elements. The reason that the memristor is so different from the other three basic circuit elements is that, unlike them, it retains memory without power. In layman's terms, this means that if you did a hard shutdown on your computer and then restarted it, all the applications and documents you had open before you shut down would still be right there on your screen when you restarted. That's an effect that can't be duplicated by any circuit combination of resistors, capacitors and inductors today, which is why researchers feel the memristor qualifies as a fourth fundamental circuit element.
In 2008, scientists at HP Labs built the first working memristor. The original idea for a memristor is credited to Leon Chua, a professor in the Electrical Engineering and Computer Sciences Department of the University of California at Berkeley.
R. Stanley Williams explains how a memristor works.
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HP as a good FAQ about memristors.
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