120VAC mains direct to DC plus 3A Current Limit

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Then you would only need about 100 uF.

Yes I was Wrong on my Calculation.

But 100 uF would give 26.5 Ohm of Reactance.
So about 3.7 Amps AC Current.

Rectifying this to DC:
Times .707 for DC Current is only 2.6 Amps

So Probably needs about 150 uF.
 
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