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

 

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.

Thanks, I have no idea what I was thinking yesterday,way easier then it I made it out to be.

 

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

Thanks, I got it, my brain wasn't working yesterday lol. I did a bunch of node analysis before hand.

 

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.

Hi,

Couldn't help but notice this is kind of a cute circuit and there is at least one simple way to solve it.

Everything seems to be given EXCEPT Vs. Since Vs determines Vi and Vs is not given, we can make Vi anything we want, and not worry about what Vs is because of that. So why not make it 1 volt (unity is often the simplest value to use).
Since the gain is 72, the voltage at the VCVS must be 72 volts. 72 volts divided by (Ro+RL) equals 9/10 amps. Since Vi=1 then the input current is 1/Ri, which is 1/1146.
The current gain is (9/10)/(1/1146) which is the same as 9*1146/10 which is the same as 10314/10, so the current gain is 1031.4 which wasn't too hard to calculate that way.

The most interesting part was that they did not specify any Vs value you had to use so that allows us to set Vi independently and not worry about what Vs became because of that. Since we knew what the input current was from Vi and Ri, we also did not need to know what the value of Rs was.

 

Hi,

Couldn't help but notice this is kind of a cute circuit and there is at least one simple way to solve it.

Everything seems to be given EXCEPT Vs. Since Vs determines Vi and Vs is not given, we can make Vi anything we want, and not worry about what Vs is because of that. So why not make it 1 volt (unity is often the simplest value to use).
Since the gain is 72, the voltage at the VCVS must be 72 volts. 72 volts divided by (Ro+RL) equals 9/10 amps. Since Vi=1 then the input current is 1/Ri, which is 1/1146.
The current gain is (9/10)/(1/1146) which is the same as 9*1146/10 which is the same as 10314/10, so the current gain is 1031.4 which wasn't too hard to calculate that way.

The most interesting part was that they did not specify any Vs value you had to use so that allows us to set Vi independently and not worry about what Vs became because of that. Since we knew what the input current was from Vi and Ri, we also did not need to know what the value of Rs was.

You might read Post #2.

 

You might read Post #2.

Hi,

Yes, I just made my explanation more explicit and with a little more explanation of why it works.