I agree. I too,have seen a 250ohm resistor used in the equipment being fed by the 4-20mA source. A multimeter on a voltage range is probably going to have an input impedance in the meg ohm range. It's loading effects would be negligible.The original poster said that the meter was set for current, not voltage.
One of the advantages of reading the voltage drop across the input resistor is that you don't have to open the circuit to take the reading. Yes, it will have, as you said some impact on the reading, but not much and not near as much as if you set the meter to current and put it across the input terminals.
I don't think the following has been mentioned yet.
Another reason for using 4-20mA signals is that it is fairly immune to noise. And, within reason, the length of run doesn't affect the signal value. As a current source the sending end voltage will adjust to compensate for voltage drop.
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