Below I posted the screenshot of the problem, and my work. Im stuck because I have 2 equations and 3 unknowns(Vs,Vi,Vo). I know its asking for the Gain of the current \[ G = Iout/Iinput \] but I figured I could solve for Voltages and just use this to figure current out. Any help would be appreciated.

 

Below I posted the screenshot of the problem, and my work. Im stuck because I have 2 equations and 3 unknowns(Vs,Vi,Vo). I know its asking for the Gain of the current \[ G = Iout/Iinput \] but I figured I could solve for Voltages and just use this to figure current out. Any help would be appreciated.

You are making things way more complicated than they need to be.

Just looking at the left side, can you determine what V_i is, in terms of i_i and R_i?

Just looking at the right side, can you determine what i_o is in terms of V_i?

If you can do those two things, can you determine i_o in terms of i_i?

If so, you are done.

 

answer is staring at you...
Ai=Io/Ii

so stop wasting time with voltages and use expressions for Io and Ii...

EDIT...

the only unknown on the right side is Vi. so what would be left side equation for Ii that uses that same Vi ? once you have both, just divide them