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For your next project you are thinking
of having a LED indicating that your circuit is powered
up properly. Your voltage regulator outputs 5V and you
decide to go for the 2V/20mA set up. How are you going
to connect your LED?

Right, you need a current limiting resistor
that will take the rest 3V. Now, from Ohm’s Law
the value of the resistor should be 3V/0.02A = 150 Ohm.
We are lucky such a resistor exists. If it didn’t,
I would prefer to get the next value up.
Vcc = V(R1) + V(D1) => V(R1) = Vcc - V(D1) =>
R1 = (Vcc - V(D1))/I = (5-2)/0.02 = 150 Ohm
Now, you may be thinking that we could possibly set
first the voltage across the LED then from the graph
find the corresponding current and then deduce the value
of the series resistor. The maths would work however,
LEDs are current controlled devices therefore the first
thing we do is set the operating current.
By the way, do you need a high precision resistor here?
I would say no, a 10% one would do, keep your budget
for something more useful. Could you place the resistor
and the LED the other way round? Yes, you could, no
difference, the voltage drop across each device remains
the same (at least under steady state). However, we
prefer having the LED close to ground for protecting
it better.
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