Take a 240V incandescent light bulb. (Don't worry, I wont tell the EU!)If 230V is applied to a 240V element, how could the current 'be a bit more'?
Measure the current at the rated voltage and again at a lower voltage. What happens?
The resistance might not be constant, but I would be most surprised to find a higher current at a lower voltage - this would imply a negative resistance or a step-change somewhere on the I-V curve.