RCD trips on an electrical leakage to earth. There doesn't have to be any loading on the circuit.
The leak to earth means the current on the live wire through the RCD is not the same as the returning current in the neutral wire through the RCD and this difference causes the RCD to trip.
Just check what connections you have in the CU. I was asked to look at a problem where the symptoms were the same after the owner had changed a MCB. On re-assembling the drop-out bus bar, he'd managed to put the pins into both live and neutral terminal of the RCB.
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