# Solve System of Equations for Mesh Circuit Analysis in S-Domain

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Ian Van Giesen le 21 Fév 2021
Modifié(e) : Ian Van Giesen le 23 Fév 2021
I am trying to solve for input voltage in terms of one current (I3 in my case). I've used KVL to derive the equations, but beyond that I'm a bit lost. I looked around at MATLAB Answers and haven't found anything. When I solve my system, I get the following response: Vi = Empty sym: 0-by-1. What does that even mean?
syms I1 I2 I3 I4 Vi s
eqn1 = (2*s)*I1 +(-s)*I2 +(-2)*I4 - Vi==0;
eqn2 = (-s)*I1 +(2*s+1)*I2 + (-1)*I3==0;
eqn3 = (-1)*I2 + ((2/s)+1)*I3 +(-1/s)*I4==0;
eqn4 = (-s)*I1 + (-1/s)*I3 + (s+1/s)*I4==0;
Vi = solve(eqn1, eqn2, eqn3, eqn4, I3)
I've inserted by code above for reference. If anyone can provide a little guidance, that would be great. Thank you.
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### Réponses (1)

Vimal Rathod le 23 Fév 2021
Hi,
The reason you are getting an empty value from the solve function is because it cannot find a solution for the given set of equations. You could probably add more equations to the set of equations by using KCL equations.
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Ian Van Giesen le 23 Fév 2021
Modifié(e) : Ian Van Giesen le 23 Fév 2021
Ah, okay perhaps I should have clarified. I am looking for the symbolic algebraic solution to this system of linear equations in terms of two variable (s and I3). I solved the problem by hand but the process was very tedious (~4 pages). @Vimal Rathod thank you for the input!

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