Confused about powering stuff from Arduino

Recently i found a video about powering motors, relays and LEDs from Arduino pins. It was said that powering things we must use diode + transistor in order not to exceed the max current. There was an example about powering LED from Arduino board (using diode and transistor). So now i am a little confused, because at the moment i have connected TWO MINI SERVOS + TWO IR RECEIVERS + 2 IR EMITTERS to my Arduino and so far they work flawlessly (all things are connected without diodes or transistors, only IR emitters/receivers have some resistors).... I havent measured the current, but i started to think that maybe one day my Arduino will burn because of that?

AND If i connect 14 BLUE LEDS (20mA 3,2V) to every digital pin, then will the microcontroller burn at sight?

Burn is rather a dramatic word but yes the power arduino pins have an absolute maximum rating of 200mA. That means the total amoun the arduino can source or sink is 200mA so 14 * 20 = 280 which is too much.

From any one pin you can't exceed 40mA and you are better sticking to less than 30mA. This is normally insufficient to power a stepping motor. Servo motors don't take much current from the arduino pins as there is electronics inside them controlling the motors from the supply but if you feed them from the +5V supply then the power is coming from the USB port or the voltage regulator chip.

Do some reading up:-

Thanks, I will.

PS. all those formulas you have there, are in diffferent letters.... for example you have written Power is expressed in Watts and is calculated from the product of voltage and current:

W = E * I

In my school, the power is calculated as P = U * I but its the same. Doesnt matter actually.