Your big capacitor has one other benefit for you. It absorbs transients from the transformer thereby protecting your RVB 50 volt bridge rectifier.
Below is unnecessary, not showing off just want to be thorough. Might as well learn all we can from an experimental oroject.
Recall i said above that battery chargers use robust rectifiers, capable of withstanding short circuits and reverse connected batteries.
They're also capable of withstanding surprising overvoltage.
When you unplug a battery charger from the wall it suddenly interrupts current through the transformer primary.
How much is that current at instant of disconnect depends on where in the sine wave the plug and receptacle break contact .
Size of the "inductive kick" or "spike" you'll get depends on how much was the current at that instant, ie how close to sinewave peak was the current when contact broke.
If the battery is still connected no sweat at all, the battery absorbs the "spike" and you have graceful shutdown.
If the battery is NOT still connected then the rectifier will be subjected to whatever "spike" the transformer produces. Something must absorb the energy.
That's why i say "Battery charger rectifiers are more robust than your garden variety bridges."
I think they are an avalanche type that survives reasonable overvoltage .
To demonstrate that effect,
yesterday while tinkering with my old raggedy charger and DMM
i connected a 10 uf motor run capacitor across output.
AC and DC voltages were about the same with 10uf as with 100 uf , about 13 and 4.5
Then to show the effect of "Inductive Kick" i unplugged the charger power cord.
The meter jumped to 110VDC and bled down over a few seconds.
Tried it again, got only 20 VDC
About 10 'unplugs' showed random DC voltages, many in the 70 to 100 volt range and some showing no spike at all..
That's not surprising because a sine wave statistically spends most of its time near peak . Sin 45 degrees is 0.71 so it spends half its time above 70%. .
I repeated with the 100 uf and never saw above 20 volts if that many, i forget...
What does that mean ? It means your charger
could make a spike that exceeds your RBV bridge's 50 volt rating.
But your 680 uf capacitor is surely big enough to absorb the energy and protect the little RBV.
Energy=1/2 CV
2
My 6 amp charger put energy = 1/2 X (10 X 10
-6farads X 110volts
2 ) = 0.0605 Joules into that ten microfarad capacitor.
That many Joules into 100 uf would be 35 volts if they all went in, some get lost in the wires and transformer...
and into 680 uf it would be only 13 volts.
So your capacitor will prolong the life of your RBV bridge.
I formed the habit years ago of always unplugging the charger's power cord BEFORE disconnecting the battery just to make life easier on my charger's internal rectifier.
There's your trivia for today...
Applying "The Basics" to everyday life is really fun.
old jim