Capacitor Power Supply for LED Use

Check with Mr. Google.

Shhhhhhhhhhhhhhhhhhhhh! People on here are trying to sleep!

That will be $1,759.34 US dollars... kindly remit immediately and the schematic will be emailed to you.

A 12 volt battery does not need a circuit diagram. Did you mean capacity or rating, not capacitive?

If you want AC mains input, the simplest circuit is a transformer.

You can connect two LEDs parallel cathode to anode with one ballast resistor or even one LED with ballast resistor (officially LEDs only have, say, 3V reverse voltage rating in the data sheet, but those indicator lamp types I have tried have very little leakage at 25V.

If you want direct current, follow the 12 volt secondary with a rectifier.

If you want DC which is steady, like a battery, you will have to add a filter and a voltage regulator.

I suggest you try searching for "transformer-rectifier" or "electronic circuits" with a web browser, then narrow it down to power supplies.

Many libraries will have elementary textbooks on electronics, there are many electronics magazines which cater for the beginner, ask the librarian for help.

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Nothing is free...

Buying one will be cheaper in the long run than building one. See your local parts supply house they have them on the shelf.