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I'm building a led cube and the guide I'm following says to use 150 ohm resistors. They are using 5mm leds but I am using 3mm leds. Would the resistors values be the same for 3mm leds as for 5mm leds? Also the guide doesn't mention the power rating or tolerance of the resistors to use. Should I get 1/4 W 150 ohm resistors?

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Resistor value depends on Forward Voltage Rating (Vf) of the LED and how much current you want to flow.
Vf changes with color - red can be as low as 2V, blue & green higher, up to  3.6V.
Ohms law determines the value. Voltage (V)/current (I) = resistance (R), so V=IR
(Vsource - Vf)/current = resistance
Driving from Red LEDs from Arduino pins at LED maximum current?
(5V - 2V)/20mA = 150 ohm

(5-3.3)/.02 = 85 ohm

Power dissipated by resistors: Power = Current * Voltage, and V=IR
so power dissipated can be P=I*I*R.
20mA * 20mA * 150 =  .06W, or 60mW.
1/8W or 1/4W resistors will be fine.

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