There is actually a use for clamping around the entire cable. Good for the typical 120V, 30A cables many of us use.
If there is a current showing on the meter then you have electrical leakage to the water. It means that there is a difference in the current between the black and the white so the field is not cancelled out. It takes a GOOD meter to do this reliably though.
Otherwise the above is dead on as what goes in must come out.
So yes, one must clamp one wire/conductor at a time for normal useage which is usually what we are looking for when checking the draw of a piece of equipment.
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