How to design a simple constant current load

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Currently, i don't have the solution to calculate the duration. I intend to measured the current consumed by microcontroller while the Vin is varied from 3.3 - 1.8V. Since the I is a known variable, based on the ohms rule V = IR, i able to figure out the impedance of MCU. Then i will apply the capacitor discharge formula where is V= Voe^(-t/CR) to calculate the duration taken for every 0.5v drop of Vcap; C is a constant ,Vo: Vcap full charge, V: V=Vcap -0.5 v. At the end, i can find out the total duration of Vcap drop from 3.3v till 1.8v.

Besides that , i already setup a hardware for testing since last week Wednesday. The capacitor values is 5F and the V cap full charge is 3.3V. It took 7 days for the Vcap to drop to 2.52v.
 

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