Measuring current and internal impedance of current source
Some ESR meters can do that. I measured the internal resistance of a 9v battery with my ESR meter, built around 1 (dual) opamp.

your circuit is unnecessarily complicated.

edit:

sorry that I just got around to this. as promised, here is the link: https://dannyelectronics.wordpress.com/2015/08/08/build-your-first-esr-meter/

it contains essentially an oscillator and then a precision rectifier whose gain is determined by the ESR of the DUT. All built around one dual-opamp.

I experiemented quite a few variations of it, but the basic concept is the same.

hope it helps.