I am working on a simple adjustable DIY power supply using an LM317 voltage regulator. J1 in the image below represents the transformer rated at 18VA, which rectified produces about 25V DC. The output range should reach roughly 12V, 1A.
Interestingly, I've found a 12V DC fan/heatsink ripped out of an old Nvidia 9400GT to cool down the LM317. I am considering one of two ways of connecting it to my circuit.
The first option is to connect it across the last large filter cap C2, with J2 and J3 representing V+ and GND connections of the fan respectively.
1) Am I correct in saying that the first option would be essentially placing it in parallel with filter cap and the voltage regulator and therefore would place it permanently at 25V, whereas the second option would drop my voltage input to the regulator by 12V, and the fan would only be at 12V?
2) What are the advantages to choosing the second option over the first?
Edit: Based on the suggestions of @AndyAka and @DoxyLover it seems that placing the fan in parallel with the filter caps is truly undesirable given the input voltage to the fan, whilst the placing it in series also causes more problems.
3) Would it then be advisable to use an additional 317 to regulate the voltage input to the fan in such a configuration?