Inverting OP AMP analysis solution problem

[sdusheyko]

Hello Physics Forums community, I'm a new member and this is my first post.

I have a circuits exam tomorrow, and though I grasp the majority of the material I'm having a hard time understanding the solution to a HW problem that I attached as a picture.

Problem: Show that the circuit has A=Vo/Vi= -k(R2/R1) where k= 1+ R4/R2 + R4/R3.

One of the issues is I have no clue how to derive: V1= -(R2/R1)VI

And also the KCL @ V1; I understand where -(V1/R2) comes from. and from where (V1-AV1)/R4 comes from. But I have no clue how the middle term, -V1/R1, is derived.
Shouldn't it instead be -V1/R3?? Could this be a typo or am I just a n00b? If so, please help me out.

Thanks very much.

 

[berkeman]

Hello Physics Forums community, I'm a new member and this is my first post.

I have a circuits exam tomorrow, and though I grasp the majority of the material I'm having a hard time understanding the solution to a HW problem that I attached as a picture.

Problem: Show that the circuit has A=Vo/Vi= -k(R2/R1) where k= 1+ R4/R2 + R4/R3.

One of the issues is I have no clue how to derive: V1= -(R2/R1)VI

And also the KCL @ V1; I understand where -(V1/R2) comes from. and from where (V1-AV1)/R4 comes from. But I have no clue how the middle term, -V1/R1, is derived.
Shouldn't it instead be -V1/R3?? Could this be a typo or am I just a n00b? If so, please help me out.

Thanks very much.

Welcome to the PF.

"V1= -(R2/R1)VI " -- Remember that the output of the opamp will do whatever it has to to try to get the - input to match the + input voltage (ground in this case). So that defines the current from the source Vi through R1, which has to ALL flow through R2 (why?)

"Shouldn't it instead be -V1/R3??" -- Yes, that looks like a typo to me too.