OK... first, do you have DrLava's Flexdrive or my Micro-Drive? You mentioned a 2.7ohm resistor, which mine has, but I don't know about the Flexdrive?
Anyway, I think you have some misconceptions about all of this.
First, current is the flow of electrons (electricity), while voltage is the electrical potential. You can measure the voltage, similar to air pressure or water pressure, with an external source, like a gauge or for electricity, a voltmeter. BUT, to measure flow, its basically the "volume" of eletrons passing any point in a given amount of time... you can only measure that by flowing electrons through the instrument. So, if you just put an ammeter (ie multimeter set to A or mA) in parallel (connected across) a resistor, the meter's internal resistance is going to act as a parallel resistor and share the current with the resistor, not giving the full current to the meter. You need ONLY the meter in line with the current to measure it fully.
The reason we say to measure the VOLTAGE across a resistor is because if you measure the voltage across a resistor of a known resistance, by Ohm's Law (already quoted here multiple times over), you can calculate current. So, if you have your 3 ohm resistor, and you measure the voltage across it, you can calculate current as follows (for example):
V = I * R
V / R = I
I = 0.15V / 3ohms
I = 0.050A = 50mA
EDIT: Nevermind about the question about the flexdrive... I see now you were talking about the inductor on there... its 2.7uH, lol. It's not a resistor, but a coil of wire wound around a ferrous core.