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RedShoe, Its hard to track the thread back and read lot of different opinions and so.
Why are you using 80 resisters? you know each resister would dissipate some power in form of heat and in turn will consume more battery?
You said you are using second method of rowan's drawing to connect LEDs, thats what I suggested.
But, when you connect 3-4 LEDs in series and attach to 9v battery you don't need the resister. The resister rowan showed is just because you are using two LEDs.
And I don't think anyone can say not to connect in parallel, whatever type of circuit it is. We always connect them parallel when we need to consume one source.
Just like, tube light, bulb and fan in your room are connected parallel to your main power supply.
Electronics is really very simple, you only need to learn 2-3 simple things.
* Ohm's Law
* Effect of series connected resisters and/or bulbs (LEDs whatever)
* Effect of parallel connected resisters and/or bulbs (LEDs whatever)
And the hobby you own is simply loveable. Why you are not into Engineering?
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