You probably could.Then I can run my relays directly off it, correct?
I wouldn't. Why?
According to datasheet Voh at 15v Vcc could be as low as
12.5V (drop of 2.5V). If @12V Voh is 10v (a drop of 2.0V)
and if your relay (just guessing) requires say 9V as an absolute
minumum to turn on, it may not turn on reliably or worse
yet, chatter.
Take it easy on that I.C.12V @ 85 ohm = 141.2mA
No need to run it at 70% of its rated capacity, even
though it will only be high for "a second".
Transistor would allow "emergency" use of any
556, including a CMOS version.
Transistors are rugged, reliable, simple to design circuit for,
plentiful, cheap.....
Whichever way you go protection/flywheel diodes are a must have.
Next answer:
For a "small signal" transistor (such as 2N2222),
For a quick and dirty value of the base resistor take
load resistance (relay coil) X 10. (When supplying
base with approx same voltage as collector).
Pulldown resistor (Base to ground) = base resistor X 10
Needed because Vol is not 0 and you need to make sure
transistor is turned off.
These values are not arrived at in the "most scientific"
method, there are formulas for this stuff that will
produce the "correct" values, but will do fine to get you started.
Edit: I'm glad to see you checked to see for yourself the paltry
source current of original 556 you had chosen.
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