AC/DC transformer question

Ok, so i bought this transformer for this UV led project im goin to make, and i dunno what to think.

Ok, so i tested a Nokia mobile charger that said 3.7V DC directly with my DMM and i got a reading of around 7V. But when i "tested" a circuit with diodes and resistors, i got 3.60 something from one end to another with the DMM.

Then i tested the one i bought being 500mA max and with regulable potential output.
So i got it to 15V and tested directly at the plug and i obtained around 18V or 19V if i remember correctly. But then i wanted to test it like i did with the nokia charger. So i hooked everything up, regulated the output to 3V, read 5. something Volts directly at the plug and then tested with circuit. I then read 3.4 almost 3.5V. Then i tried the 4.5V and across the plug i got 7V if i reckon correctly, and when i measured in the circuit i got around 3.8 or 3.9 (but doin maths really quick in my head, i think it goes over the 500mA max of the transformer, so i think this value is alright).

But when i measure the plug of my laptop's AC/DC transformer, i read the 19V exactly (well i get 18.80/18.95V).

So i dont know if to trust or not the transformer/ratings they announce.

Also i didnt want to buy rheostats (aka potenciometers) as they are more expensive than the resistors.

LED Calculator - Current limiting resistor calculator for LED arrays i used this to simplify the math...the maths are very simple, but at least i got someone drawing for me
but i was thinking in using around 10 to 15 LEDs with forward voltage around 3.3V, and an input of 12V and LEDs in the range of 20mA to 40mA(see below)
I was also thinking in geting a pot after the Vdc (before the parallel LEDs) so i can regulate the current on the LED's, making some voltage to go to this pot, and droping the voltage at the parallel circuits. So 0ohm at the pot would make the 40mA and a "max" would make the 20mA. But i also cant figure out if that is goin to work like that or not.
After some drawings and simple math, i got into some values, but i still didnt know if i was thinking in the right way (thinking that the circuit would react like i described: what if it doesnt react like that)


i still want to run a few models on the PSpice program, but id like to know what the DIY and circuit experts around here think about this. It just takes the time to read, as this isnt mind-boggling problem.

Thanks all for reading,
José

Usually wall-wart type transformers, such as your Nokia charger, are not very well regulated. If there is no load connected, the output voltage is usually much higher than the rated voltage. When you connect a load that draws the transformers rated current, the voltage will more likely match the rated voltage. Additionally, most wall-wart type transformers I've tested have a pretty noisy output. One of my 12v transformers outputs 16v w/no load and has a nearly 1v ripple. If you want better regulation, I recommend using a LM317 with bypass capacitors to smooth the output of the transformer.

More expensive power supplies, such as your laptop charger, are usually better regulated than the cheaper wall-wart types, and therefore output closer to its rated voltage.

Hope that helps,
Spectral

thank you...that really helps... After a while and a bit of thinking, when im goin to buy the resistors, i'll just ask a 1kOhm resistor first to the store guy, test the circuit, and check what voltage goes for the resistor, and then do some quick math with my cell phone and get the resistors i need...