Finding a voltage in an ideal op amp.

[gunnerrex]

Homework Statement

Hello everyone. I tried solving this ideal op amp for V0 but kept becoming confused because of the structure at the bottom. I only have experience solving ideal op amp questions when they are grounded and have not encountered one like this before. All the data is given in the picture of the ideal op amp I made in photoshop. I believe the curved line behind the second stage means that it does not come into contact with the wire it passes.

Homework Equations

The only method I have for solving ideal op amps so far is nodal analysis. I am guessing that is what must be used to solve this ideal op amp as well.

The Attempt at a Solution

When I tried solving for V0 I got zero. I don't understand how to handle the bottom nodes. I drew the picture as given to me and have not labeled the extra nodes, but here is my attempt going from right to left of the ideal op amp:

(V0 - Va) / 10,000 = 0
[1] so V0 = Va

(Va + V2) / 5,000 + (Va - V0) / 10,000 = 0

[2] so 3Va + 2V2 - V0 = 0

(V2 - Vb) / 100,000 = 0

[3] so V2 = Vb

(Vb - V1) / 25,000 + (Vb - Va) / 100,000 = 0

[4] so 5Vb - 4V1 - Va = 0

and finally Vc +V1 = 0

[5] so Vc = -V1 = Vb because of ideal op amp rules.

After working backwards I get V0 = 0 volts, but I doubt this is right.

 

[Zryn]

Could you label Va and Vb on the diagram?

Given the two ideal op-amp rules relating V- to V+ and I- to I+, what can you deduce regarding the voltage at the inverting input of the second op-amp, and thus at non-inverting input of the second op-amp?

How does this relate V0 to V2, and thus to V1?