How can 12ma illuminate 3 LEDs in series as brightly as 48ma can illuminate 3 LEDs in parallel?
If you use a multimeter, you will find that the voltage across the current source with 3 LEDs in series will be around 5V, but if you measure the voltage across 3 LEDs in parallel, the voltage will be around 1.5V.

The answer to your question is that if you push the same amount of current through each LED (15mA in both cases!) the voltage will settle so that the same amount of power is used.







simulate this circuit &ndash; Schematic created using CircuitLab

This property where current splits up in parallel devices and is equal in series devices is related to Kirchoff's Current Law, which you can read about. It is something like the law of "conservation of current"... current is never created or destroyed, it just loops around and comes back to where it started.

However this,


  Next I connected 3 LEDs to separate 16ma 9volt current source. I measured the total current and found it to be 48ma.


can't happen. A 16mA current source will put out 16mA. A 9V voltage source will put out 9V.

A current source will adjust its output voltage* to ensure the current stays where it's set. A voltage source will adjust its current to make sure the voltage stays where it's set.

*Unless it's a really crappy current source, like a battery and a resistor!