I have a motor for a submersible pump with a Rated Current of 8.4A as given in the motor's electrical data. However, when it is running, I record a current of 3.4-3.9A. Is there a fault I am supposed to look into, or is this normal? Why is the rated current so much more than the measured current.
The "rated" value is the maximum safe value for each parameter, not necessarily the actual value for any particular working condition.
The current when the motor is running will depend on the load. If you were testing it with no load, the current will be lower.
Presumably the pump specification (not the motor spec) will tell you the conditions (flow rate, pressure head, etc) that make the motor work hardest. You could try simulating those conditions and measure the current again.
FWIW the numbers from the data sheet are consistent with each other. For the minimum voltage (200V), 8.4A current, and a power factor of 1.0, the calculated power input is 1.68 kW compared with the data sheet value of 1.65kW.
This can be due to the rated current is showing the initial start current which can be greater than the running current.
The supply needs to be fused to cope with the start current as, if you put a fuse matched to the running current, it would blow on start-up.
You probably won’t be able to measure the start ( or in-rush) current with that meter, you would need something more accurate.
Did an experiment about the current through an incandescent bulb, measuring the current v time - the in-rush current is much higher for initially and reduces rapidly as the bulb heats up - talking 20 to 30ms here iirc.