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Can someone please tell me a general, universally applicable definition for cathode and anode, that I can always use to recognize one or the other?

In a cathode ray tube, electrons are emitted from the cathode. In a battery, electrons are absorbed into it, except when the battery is charging where it is the opposite. It gets very confusing.

What is the origin of these terms?

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You don't have a universal definition. Anode and cathode are very old terms coined by Faraday and their etymology is not that helpful.

The negatively charged terminal of a battery or DC power supply is the cathode. This refers to the electrostatic sign. The particular electrode so connected to that power terminal is also the cathode e.g., in the cathode ray tube.

In electrochemisty, cathode is the always electrode where reduction is occuring. Its electrostatic sign can be positive or negative. This applies to DC current only. Similarly, anode is the electrode where oxidation is occuring. I remember them as a(node) and o(xidation) are both vowels. C(athode) and r(eductio) don't start with vowels.

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