So back to the theory…

I have dealt with this circuit before and I am dealing with the initial case where there is only one led. D1 and R1. As memory serves what is true for one led is true for multiple leds.

I consider that the resistance of leds is less than an ohm so it does not exist in my theory…

LEDs are a current limited device. So for the purposes of theory in circuit comparison current will be call I.A and current will be constant

We will vary the input voltage

V2=2*V1; V2 is two times the size of V1.

What is p1 and p2 given I.A is constant in both circuits?

V=IR;

P=VI;

P=(V^2)/R ; power dissipated by the resistor and assumed to be power turned into heat.

; energy can be neither create or destroyed. Thus I am assuming the resistor is turning the energy in joules or calories of heat.

sub-question B what is R1 and R2?

V2=I.A*R2; Given ;subB line1
V1=I.A*R1; Given ;subB line2

V2=2

*V1; Given ;subB line3*

V2>V1; it makes sense but I forget the math property ;subB line4

V2=2V1; Given…V2 is two times the size of V1. ;subB line5

V2>V1; it makes sense but I forget the math property ;subB line4

V2=2

I.A

*R2=2*I.A

*R1; substitution B line1 and B line2 into B line 3 ;subB line6*

(I.AR2)/I.A=(2

(I.A

*I.A*R1)/I.A ;dividing both sides equally ;subB line8

R2=2*R1; Math ;subB line9

Section A

P1=(V1^2)/R1; Given ;A line1

P2=(V2^2)/R2; Given ;A line2

P2=((2*V1)^2)/(2*R1); Substitution A line2 and B line5 and b line 9 ;A line3

P2=(4(V1^2))/(2*R1); Factoring ;A line4
P2=2*((V1^2)/R1); Division ;A line5

P2=2*P1; Substitution ;A line6

If I replace the 2 with variable N(where N is any number) we can kind of get the idea that the power consumed by the resistor varies with input voltage. The current must be constant so we do not destroy the LED nor let the LED dim un-necessarily. The current going through the led determines the intensity of the LED.