RC

[MrAl]

Hi again,


A lot of times when you have two parameters that seem to be able to vary one
of them ends up being dependent on something else too. For example, one
resistor value may be the coil ohms instead of an actual resistor and so
you have to go with that. In times when they can both vary then you have
to ask yourself if something else enters the picture too which helps to fix
or limit the range of one of the two parameters.
Of course sometimes we want to study the effects of BOTH parameters varying
and for that we would simply resort to moving to a dimension one more than we
are currently working in. That is, we would look at several values of say R and C
letting R vary from say 100 to 500 ohms in steps of 100 ohms and for each R
we let C be maybe 500uf to 2000uf (500uf steps) and consider the results from all of these
combinations. For that example of R and C, we would end up with 5 values for R
and 4 values for C, where each value of C is used with each value of R. This would
result in a total of 4 times 5 or 20 different results which we could look at and
this might give us some more insight for picking the right two values, or it may
simply suggest that any combination of values would work as long as the time
constant or other objective met some criterion, or maybe even a range for R and C.
If the time constant ended up being a constraint in the application, then our values
would end up being constrained to T=R*C which means that although we might be
allowed to vary R from 100 to 500 ohms, we would have only one value of C that
worked with each value of R. Thus now instead of having 20 results to consider
we would only have 5 different results to think about.
If you have some particular application in mind we can look at that in more detail and
perhaps come up with some more exacting data.

The max power of the 180 ohm resistor depends on the max voltage and the
max time it has to run at that voltage and the duty cycle, however if the
resistor is to be run at some voltage V for several minutes then it's a good idea
to rate the resistor according to the max voltage that will ever be encountered.
That would of course be P=V^2/R and that's the easiest way to do that.
If it does indeed vary quite a bit then you would have to resort to calculating
the average power using the integral to calculate power over time. Of course
if you dont want to do that you can also try experimenting a little as long as you
allow ambient to go up to the max that will be encountered in the final application.

Before i forget, there is one more little point about driving a RELAY with a resistor
and cap. That is that if the cap delays the turn on or turn off of the relay then it
is entirely possible that it causes the relay contacts to open or close too slowly.
This happens because the voltage to the coil does not suddenly increase or
decrease but builds up slowly over time and the armature does not move as fast
as if it was driven directly with a fast changing drive signal.
This can be a problem if the contacts arc over as it takes longer to extinguish the
arc if the cap charges or discharges too slowly. Sometimes you cant actually do
it that way, but have to resort to a little switching circuit with at least one
transistor to drive the coil while the cap and resistor end up on the base of the
transistor. The upside to doing it this way is not only faster contact switching but
also the ability to use a much smaller capacitor value and thus save cost that way.
The cost of a small transistor and small cap can often be cheaper than a larger
cap, and might save from buying a power resistor too. Something to think about.
Of course a slightly more complex circuit with a little hysteresis is even better.

 

[Electronman]

Thanks Man,

They way I knew before for a such 2 variable circuits (ie Resistor and capacitor are not definite) Is to consider ONE of both known (determine it by myself) and then try to put those both in the related formula to find the other, Know I want to know how engineers handle a such situations? Our circuit in this thread is one which has a such problem when designing, Even If we have Vc and Vs and t but yet there are TWO unknown parameters (cap and the resistor) I want to know if an engineer uses my way to solve it or he can use a 2th order equation to solve it (I do not know if it's possible anyway?).

considering to Power, you can see that our circuit has a time constant of several seconds, so do we need to calculate it by integrals? If so Can you let me know it for our circuit here?

I did not get your last paragraph, Are you talking about the ability of the relay for FAST switching (I have heard that most are able to switch as fast as 500 to 1000 times per second), Or you are talking about disability of caps and inductors to change their voltage and current suddenly?

Many thanks for your time.

 

[MrAl]

Hi,


If the equations are linear than we can sometimes use simultaneous equations to find
the answer to the two variables. Other times we can use what is known as
"constrained minima and maxima" when there is some kind of constraint on the equations.
What exactly is it that you want to calculate?

I dont think you need an integral here but then im not entirely sure what it is you
intend to do. If you feel you need an integral it is:
Pavg=1/(t2-t1)*Intg[t1 to t2]p(t) dt
where
"Intg[t1 to t2]" means integrate from t1 to t2 and
p(t) is the power which is often p(t)=v(t)*i(t).

In the last paragraph of my previous reply i was talking about the possibility of
causing a problem when driving a relay coil with a cap and resistor for the purpose
of either oscillating or for delayed switching. The contacts like to open as fast
as possible and a cap across the relay (if that is what you intend to do) can cause
slower contact movement which in turn causes more arcing which causes faster failure.

 

[Electronman]

what I just want to know is about knowing the max power consumed by the resistor to choice a suitable resistor to do not lose my resistor, At first I thought I can use formula "P= Vmax^2/R" for our current circuit but you told that It is not so good.SO what's your suggestion as an Engineer? What Do engineer do at these situtions when they are designing such circuits?
I am not sure about both R and C when they are unknown? I want a an engineering view.

 

[MrAl]

Hi again,

We need a circuit here. Post a circuit and note what you want it to do and we'll
take it from there.

As i said before, you could simply calculate the max voltage the resistor will ever
see and then use P=V^2/R. There's nothing wrong with doing it that way.

For example, if we have a resistor of 1000 ohms and a cap of 1000uf (or any value
for that matter) and we have a supply voltage of 12v and the cap charges up
with the resistor in series with the cap, since the max voltage is 12v and the
resistor is 1000 ohms then we can use P=V^2/R which in this case would be
P=12^2/1000 which would come out to P=144/1000 which is equal to 0.144 watts.
Thus, a quarter watt resistor (0.250 watts) would suffice.

If the 12v pulsed on and off then we might want to use the integral to calculate
the power in the resistor, but you should know that this power calculation will
always yield a wattage that is less than the calculation above with 12^2/1000
because a pulsing circuit has a duty cycle that is less than 100 percent.
The way we would do this though is we would have to calculate the voltage
and the current through the resistor over one period, and then use that in the
integral i posted previously. The voltage calculation would yield a function of
v with time like V(t) and the current calc would yield a function of i with time
like I(t), so within the integral we would use p(t)=V(t)*I(t) and we would
get the answer. Again though, this calculation would come out with a power
rating that is less than using the max voltage, and so if the cap ever shorted out
(a very possible failure mode for capacitors) the resistor might burn up and cause
smoke and/or fire.

 

[tresca]

why do you want the RC time constant. In this case, I think you need the RL time constant.

You would need a 2nd order differential equation or like people have suggested, build it, test it, tweak it, use it.