Charging batteries directly from 117 volt wall socket
117VAC is a sinewave that rises up to a peak of \$\sqrt2\times 117 = 165.5V\$ then back through zero to a negative peak of -165.5V then back through zero and repeats.



How does this allow you to charge a battery of 117V even if you rectified it - you'd still get peaks of about 164V falling to zero then back up to 164V.