Switches/Relays require some initial current to break the oxidation layer that is formed across the contacts. Supplying this amount of current helps the contact form reliably. The current supplied heats the oxide layer. This amount of current is obviously an additional burden on your power circuit but is the minimum current required to form a contact. Oxidation generally happens in humid conditions where the oxide layer is formed across the joints. The oxidation can generally be treated as resistance when you speak as an electrical engineer. The scenario of wetting current can be seen in the case of switches where you provide the stimulus but still doesn't turn up, where little more current would have been required there. Generally, in the humidity tests, these kind of issues come up on the board. The amount of whetting current depends on the material that is used for the contacts. For example, a gold plated contact may form a reliable contact with less wetting current. the two generic circuit parameters you may across in this scenario are punch through and stand-off voltage. Stand-off voltage is the minimum voltage that need to be provided for the oxide layer to break through.
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