I want to solve the following time-dependent system of equations:
Clear["Global`*"];
q = (((1602176634)/10^9))*10^(-19);
k = (((1380649)/10^6))*10^(-23);
\[Eta] = 3/2;
Td = 20 + (5463/20);
R1 = 10;
Vi = Piecewise[{{u*Sin[\[Omega]*t],
0 <= t <= ((2*Pi)/\[Omega])/2}, {0, t > ((2*Pi)/\[Omega])/2}}];
u = 230*Sqrt[2];
\[Omega] = 2*Pi*50;
Is = 5*10^(-9);
FullSimplify[
Solve[{I1 == Is*(Exp[(q*(Vi - V1))/(\[Eta]*k*Td)] - 1),
I1 == Is*(Exp[(q*(V1 - V2))/(\[Eta]*k*Td)] - 1), I1 == V2/R1}, {I1,
V1, V2}]]
But it spits out nothing, just the simplified version of the input. Is there a way to solve for the unknowns $I_1$, $V_1$ and $V_2$?
Vi
is a function oft
but I can not see anyt
in your equations. $\endgroup$Vi
is to be treated like a constant in your equation, then replace it by a symbol without value ( e.g.Vi0
), then solve the equations and replaceVi0
in the solution byVi
$\endgroup$