Why is my MOSFET switch not behaving as expected?

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saad87
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I have the following circuit wired up on a protoboard.

Schematic of an N-channel MOSFET switch: 3.3V supply through R1 1K to Output node, Q1 BSS138 drain at Output, source to GND, gate fed from R2 1K input with R3 27K pull-down to GND.


The datasheet for the BSS138 MOSFET is here. I'm puzzled regarding what I'm seeing happen with this circuit - when I apply 3.3V at the gate resistor, the MOSFET turns on fully and I see 3mV at the output. This, of course, is expected.

However, if I remove 3.3V from the gate resistor, the pull-down resistor turns the gate off. I expected to see approximately 3.3V at the output, yet I only see 2.7V. If I replace the 3.3V on R1 with 5V, the output shows 4V. In other words, a volt is being dropped on R1 when the MOSFET is off. Is this expected? Somehow, I expected the MOSFET to have an immensely high resistance when off and hence expected approximately 5V being dropped on it when it's off.

Are my expectations wrong for this MOSFET?
 
What is the Output tied to . . some kind of load?
 
One way this could happen is if you used an analog voltmeter to do the measurements.

If it drew about 1 mA while taking the measurements, you would get voltage readings like this..

It could also just be a faulty FET.

One easy test would be to put a milliammeter in series with the supply and see if you can cut off the current when the gate voltage is dropped to zero.