Find Vout for Op-Amp Circuit with Attached Image

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SUMMARY

The discussion focuses on calculating the output voltage (Vout) for an op-amp inverter circuit. The user correctly identifies that with Vb grounded, both Va and Vb equal 0. The derived equation, -Vin/R1 - Vout/R2 = 0, simplifies to Vout/Vin = -R2/R1, establishing the gain of the circuit. With R2 equal to R1, the gain is confirmed to be -1, resulting in an output voltage of -5V for the given input conditions.

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1. Please refer to attached image.



2. The attempt at a solution.

I noted that Vb was grounded and would therefore be equal to 0 and because one of the two op-amp rules states that Va = Vb, both will be equal to 0.

I wrote an equation at node Va:

[Va - Vin]/R1 + [Va - Vout]/R2 = 0

Because Va is 0, the equation simply became:

-Vin/R1 - Vout/R2 = 0

And plugging in the given values for part (a), I acquired - 5V. I'm not sure if this is correct or not as the book does not have a solution manual available yet.
 

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-5V is right. In this configuration, the circuit is an "inverter".
 
Thanks! I was just wondering :)
 
Just for completeness...

Take your equation...

-Vin/R1 - Vout/R2 = 0

then rearrange it to give..

Vout/Vin = -R2/R1

where Vout/Vin is known as the Gain.

a) R2 = R1 so Gain = -1
b) etc
 

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