Reading a 120V AC powered relay state: problem with noise?

Other Hardware General Electronics
21

From the same Wikipedia link, it says

These are the formulas I used. For s, the complex frequency, I was looking at it when the sinusoid is in the first quadrant (j=1) and Vin = 120V rms and w=60Hz.

In relation to the RC series circuit at the link and its formulas above and when looking at it as a voltage divider, wouldn't
VR(s) + VC(s) always = Vin(s) at any point in time?

Actually, I prefer (and should have) looked at it as a passive RC Low Pass Filter, as this uses the standard and intuitive approach for calculating Vout.

22

You have been given formulae, you need to use them as they are given.

The term "s" in the formula is specified as for the Sinusoidal steady state which is of course what we are dealing with here. Now "j" is not a variable for which you can substitute random values at will; it refers to the "imaginary" unit (also called "i") and you have to use that ("complex") value in any equation if Excel will handle such. (Will it?)

Also, "" is not "60 Hz", it is 120? (120 times pi) or about 377 radians per second, which is why your estimates of the reactance of the capacitor are so far awry.

23

XC = 1 / 2pif*C
the impedance (z) is the square root of (R2 + XC2)
(I know, it's -j, but there's no XL to contend with.)

current = v / z

the voltages across the components do not add up to the source voltage, unlike with resistors

R2 !