Inverting Op Amp Circuit: Calculating Output Voltage with Feedback Loop

[AdkinsJr]

Homework Statement

Write output voltage in terms of input voltages for the circuit drawn.

I drew the circuit and then feed back loop.

Homework Equations

Ohms Law V=IR
Basic Properties of Op Amps (ideal), voltages are assumed equal at both inputs...

The Attempt at a Solution

The difficulty is that there should be two currents that need defining, but I'm not sure how to eliminate both of them. I wrote two equations for the current through the feedback loop and then equated to write Vout in temrs of the resistances and Va.

I_a = \frac{V_{out}-V_a}{R_2}
I_a = \frac{V_a-V_{out}}{R_1}
V_{out}=\frac{V_a-V_{in}}{R_1}R_2 +V_a

I can't figure out how to write Va in terms of Vin and the resistances at this point. The only other relationships between Va and other quantities come from the fact that V_b=I_bR_3 which means that V_a=I_bR_3 also, but I still need to get rid of the current Ib now, so that doesn't help much. I can't figure out what I'm missing. Any help would be great.

 

[AdkinsJr]

There's a mistake in the feed back loop in my drawing, the ground at the end of R2 should not be there, that should be Vout.

 

[gneill]

You've listed one useful property for the op-amp in a negative feedback situation. What other property might be useful?

 

[LvW]

Have a look on the second equation. Obviously, it is wrong (Vout mixed-up with Vin).
More than that, you can forget the influence of R3 (because an ideal amplifier with infinite input resistance is assumed). Hence, you can set Va=Vb=0.