A microampere current can be measured by passing it through a resistor and measuring the voltage. Placing a series resistor for measurement will affect the source insignificantly if this resistance is say 1% of the source resistance. So in some cases, the resistance can be even 1 meg, and measuring the resulting 1V is pretty easy. One can today measure voltages as little as a few microvolts. that means 1pa and 1meg or 1nA and 1k etc. Consider a 1uwatt in a resistor of 10k. Current is 10uA. voltage is 100mV. So this is easily done. 1uwatt in 1meg will mean 1uV,and can be done.  At specific frequencies, one can also measure 1nW or even lesser. All sources have a resistance associated with them, and high resistance sources with low voltages are the most difficult to measure. One can use lock in amplifiers for ac. without knowledge of how the vibration is converted to electrical signals, it is difficult to make useful comments.  For further discussion.. contact  me at [email protected]

Thank you Dr.Mani.

For 1uV, the currents are 1pA for 1meg and 1nA for 1k. Pl see correction.

charge amplifier perhaps can help you...

Use simply a current to voltage convertor with good OPA.

Thank you Mr. Jie Tang

Thank you Mr. Josef

I have run into a similar issue with my work where I am measuring low-voltage and current values from a small form factor indoor solar cell. I opted to use a sense resistor with a low ohm rating (ohms to 10s of ohms) and measure the voltage difference across the resistor. I needed to obtain current and voltage values during operation to calculate the efficiency of a circuit so a large resistance wasn't practical for my work. I used a 16-bit ADC in conjunction with an Arduino to obtain measurements, see "https://www.adafruit.com/product/1085". This link describes how to use the 16-bit ADC with the Arduino in good detail. I hope this helps.

Thank You David Newell

Hello Everyone,

I like to thank everyone for their answers. I have also ran into the similar problem. I am working on electrowetting energy harvesting. A very small scale AC current is expected to be generated by mechanically modulating an electrolyte onto a substrate. I am trying to measure this AC current simply by using a series circuit with 10K resister and a Keysight DMM. At one point, I even simply connected the electrodes from the harvester directly to DMM and measured the ACI (AC current). At this point, I am not sure if either of these approaches are correct to measure micro-Amps level of current? I appreciate any insights on this. Thank You all.