Op-Amp Output Voltage Calculation with Two Input Voltages

[mad_monkey_j]

Homework Statement

Derive the expression for the output Vo in terms of the input voltages V1 and V2?
Attached image is the cir

Homework Equations

Inverting amp:
A=Vo/Vi=-Rf/Ri
Vout=-Rf/I_2

The Attempt at a Solution

No idea how to go about this question with two input voltages.

 

[gneill]

If there was only one input voltage (and input resistor), what voltage would you expect to see at the - input of the op-amp? What current flows into the - input terminal of the op-amp?

 

[mad_monkey_j]

The current across R1
V1/10k
The current across R2
V2/5k

So I1 is V1/10k +V2/5k?

 

[gneill]

Okay. Presuming that you understand why this is so, can you proceed to state the expected output voltage as a function of the inputs?

 

[mad_monkey_j]

so Vout = -Rf*(V1/10k +V2/5k)?

 

[gneill]

You sound surprised. Yes, that is the logical consequence, is it not?

 

[mad_monkey_j]

yea didn't think it would be that simple tbh, i was thinkin it would be huge although i didn't know where to start either.