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The current rating of a contact is defined as the current level that creates a certain temperature rise of the contact spring — usually 20°C or 30°C. Both electrical and thermal factors govern the heat created by the current.
The maximum switching voltage of a relay is the maximum voltage that can be across the contacts whether the relay is open or closed. Operating a relay with high voltages present can cause arcing, and this in turn erodes the contacts and eventually degrades contact performance.
A current coil is basically a coil, such as, a wire wrapped around an electrical conductor.