If i have a circuit with voltage sources of 50v, 10v, 40v and a current of 5a all connected in series, how do i know if the circuit is valid or not valid?

Well I'll tell ya.  I've had a piece of paper that says I'm an electrical engineer
for 43 years now, and I've done a lot of stuff with volts and amps during that
time.  But you just threw something at me that I don't recognize.  I don't know
what it means when somebody says that a circuit is 'valid' or not valid.

I'm taking your points, so I'll give you an off-the-cuff, back-of-the-cocktail-
napkin answer, straight from the seat-of-my-pants department:

The circuit you described has voltage sources and they're connected
in series.  So far, so good.  You have current in the circuit, so you know
that the circuit is 'closed' (continuous).  The current is reasonable (5A,
so you know that the circuit is most likely not 'shorted'.

We can't say anything about the net effective resistance in the circuit,
because we don't know the net effective voltage.  IF all the sources are
connected up with their pluses and minuses all facing the same direction,
then the total voltage is 100 volts.  But it's possible that one of them is
connected in the opposite direction ... like if you put one battery in your
flashlight upside-down.  If that happens, then the voltage of that source
adds to the voltage of the other two sources as if it's a negative voltage,
and the sum of the three sources will be less than 100V.

As long as each source is capable of delivering 5 A ... possibly negative ...
then your circuit sounds perfectly "valid".  The description is pretty sketchy,
but there's nothing in it that won't work.

If there's a new definition of circuits out there that I haven't heard yet,
then this is a pretty useless answer, and I apologize.