I want to solve a three-equation system, but I need to constrain two of the variables so that they can only take one of several discrete values that I would specify (this is a circuit design problem where I need to find a resistor that can have a continuous range of values and two standard capacitors). I attempted to use Solve[] using the logical OR operator || to constrain the two variables, but Mathematica tells me that the system is not a quantified system of equations and inequalities. Does anybody know of a solution to this?
Here's the code:
Solve[{
(10*^3 == 1/(2*Pi*Sqrt[10000*r2*c1*c2])),
(20 == 3*Sqrt [r2*c2]/Sqrt[10000*c1]),
(3 == Sqrt[r2/10000]*Sqrt [c1*c2]/(c1 + c2)),
(r2 > 5000),
(c1 == (10*^-12) || (100*^-12) || (22*^-12) || (0.001*^-6) || \
(0.01*^-6) || (0.1*^-6)),
(c2 == (10*^-12) || (100*^-12) || (22*^-12) || (0.001*^-6) || \
(0.01*^-6) || (0.1*^-6))},
{r2, c1, c2}]
x == (1 || 2)
doesn't make sense (within Mathematica) but(x == 1) || (x == 2)
does. You can omit the parentheses from the latter. If you use only exact numbers (i.e. there's no decimal point in them), thenReduce
should theoretically work, but it's taking a very long time on my machine. $\endgroup$c1
andc2
, you only have one variable to solve for:r2
. Do you have any reason to believe that all three equations will be satisfied for some value ofr2
? The system looks overdetermined. $\endgroup$