how to calculate value of Vs if Qs+Qsc=0
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Qs=-e*(1+Ga*exp(-(Ecs-Eas)/K*T)*exp(Ecb-Ef)/K*T*exp(-eVs/K*T))^-1
Qsc=sqrt(2)*(Nb+Pb)*e*Ld(cosh(Ub+eVs/K*T)/cosh(ub)-(eVs/K*T)*tanh(Ub)-1)^1/2
if Qs+Qsc=0
calculate Vs
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John D'Errico
2017-7-9
First, I must assume that eVs is what you mean by Vs, because there is NO variable Vs in those equations.
So next, assuming all of those other variables are unknown symbolic coefficients, then no analytical solution will exist. I doubt I even need to check that.
Nothing stops you from putting it into the symbolic toolbox and checking. Just add the two right hand sides. You then have ONE equation in the variable Vs. See if solve gives a solution.
Only if all of the other variables have KNOWN numerical values will it be possible to search for a solution. Again, just add the two right hand sides, and use fzero. Choose a decent starting value, as there may be multiple solutions. I don't expect infinitely many solutions here, but there may be two or three at most, depending on the other variables. I can't plot it to make a better guess though.
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