Do we use an active or passive rectifier to convert AC current to DC current, and why?
It really varies. The electricity in your outlet is ac, so the rectification is done in the product. You can either rectify passively, using just diodes, or actively, using triacs or mosfets. Diodes are nearly always used since they are the cheapest and simplest solutions for small currents. Once you reach too large currents, then the forward voltage of the diode will generate too much waste heat, resulting in the use of active rectification using mosfes or triacs. You generally see active rectification in very high current enviorments, or other exotic applications. Mosfets have less waste heat at high currents due to their low rdson, or baisically their resistance when conducting, and they have no forward voltage, compared to a diode which has a voltage drop but negligible on resistance.
Current squared times resistance is for mosfet power dissipation when just concerned about on resistance Current times voltage drop is power dissipation for a diode when just concerned with forward voltage
Edit: woops, i forgot to include power factor correction, or pfc, as one of the normal uses of active rectification.
Diodes are used at voltages where they are a small contributor to power loss.
At very small voltages (e.g. 6V 60Hz AC obtained from a transformer) one could conceivably use MOSFETs which lower the voltage drop, at the cost of complexity.
At moderate to high power levels (upwards of 1000 watts), thyristors (SCRs, triacs) are commonly used, because they can block in both directions and can be used to avoid surge currents into DC link capacitors.