i got 2x of the transformers similar to what you have in hand only with single secondary winding
baically
at the worst case situation ::
- the core material quality or the overall design is not (yet proven to be /!\) dangerous but it is below average e.g. :
- the efficiency is about 5 to 15%
- they heat up losing more power to increasing coils resistance
- from ohms law E=ir+U=i(r+R)=u+iR the useful power at R is maximum** at r=R e.g. u=U as E=u+U
E=2U in this case** -- the output power would be half the total or the same dissipated at r (at inside the supply) also the voltage would be 4.5V for E=9V
- this is not idealized power source but a transformer
a transformer in turn has a property to output more power to the lower load resistance - in other words
the more power you drain from transformer the more power it outputs . . . up to a critical point - yet in another words
IF in a case of ohmic power source the max output power is occurring at r=R THEN with a transformer the lesser the R the less becomes and r . . .
. . . what i have experienced is the peak *** power output for 9V transformer is somewhere (very approximately) below 4V *** (did this test quite long ago)
your option is to use series 18V output (or if it's 2x4.5V a voltage doubler ) -- the most efficient is however a full wave rectifier - a 4 diode bridge
the practical output for my transformers 9V 300mA was some 50mA at 6V up to 300mA at near/below 4V *** (e.g. the particular chinese TF labels has the max possible values for either AC voltage or AC current but not simultaneously)
the nokia cell phone transformers 3.7V out (newer models) have efficiency around
50% (the best i've seen so far)
also the best (?a magical?) voltage transfer ratio for a line transformer (in a means of efficiency) is according to my statistics about 10 to 12
e.g. (that is) for 240V input it's 20 to 24V output with full wave rectified it is multiplied by that
max. 28 to 34V direct current output
so if you can configure 18V output it is l-i-k-e-l-y the best setup for your TF
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the electrolythic capacitors likely tolerate some excess to nominal - this is what i think - i never seen capacitor heating up at dc circuit or as a filter cap to rectifier bridge (as they are temperature rated 85°/105° C you don't want to spend any extra time at soldering them)
i have seen a rectifier bridges that have a reverse leakage/conductance/breakdown before the rated max.revese voltage -- because of that i always use 1N4007 for self built bridges , when required in series parallel or both with near matched alternate conductance shoulders for rectifiers