Unsure of finding Vout for this Opamp

[whatphysics]

Hi there, these aren't homework questions. I came across them during revision and couldn't solve them. So any help would be appreciated. The ans for the 1st image is 2 and second image is 3.

For the first image, I attempted to calculate the Req for 10k and 20k resistors connected to V1 since they are parallel. And then to get Vo, I took (1+R2/R1)(V1) but I got (1+2)(1)=3 instead. Where have I gone wrong?

For the second image, i tried using superposition principle by killing 2V to get Voutput due to 1V then killing 1V to get Voutput due to 2V. I got Vo(due to 1V)=(1+20/20)(1)= 2 and Vo(due to 2V)=(1+20/20)(2)= 4 so adding them would be 6V but the answer is 3V.Where have I gone wrong?

Thank you for reading this and helping me!

 

[LvW]

First Figure: For which purpose do you need Req?
There is a simple voltage divider at the non-inv. input (20/30=2/3) - connected to an amplifier with the gain(1+2)=3.
Hence, the overall gain is (2/3)*(3)=2.

Second figure: With superposition (same principle with voltage division) we have
2V*(1/2)*(1+1)=2V and 1V*(1/2)*(1+1)=1V.
Hence, Vo=3V.

 

[jim hardy]

The ans for the 1st image is 2 and second image is 3.

That's the answers, so i guess the question was "what is Vo?" as in title of thread ?

The way that always works for opamps is this
Write KVL for voltage at opamp's + input.
Write KVL for voltage at opamp's - input.
Set them equal, solve for Vo.

1st image:
Vat +input = 2/3 , do you see why ?
Vat - input = Vo/3 , do you see why ?
equate them, 2/3 = Vo/3 ,
multiply both sides by common denominator of 3 and you get 2= Vo, swap sides to get Vo=2 .
It's that easy .

2nd image
Vat +input = 1.5 , do you see why ?
Vat - input = Vo/2 , do you see why ?
equate them, 1.5 = Vo/2
multiply both sides by 2 and you get 3= Vo, swap sides to get Vo=3 .

The KVL equations for V at + and - inputs are seldom so convenient as in the examples you gave,
but that method always works and you ought to practice until it becomes intuitive.

Thoreau didn't know he was giving electronics advice when he wrote "Simplify Simplify."

old jim

 

[whatphysics]

First Figure: For which purpose do you need Req?
There is a simple voltage divider at the non-inv. input (20/30=2/3) - connected to an amplifier with the gain(1+2)=3.
Hence, the overall gain is (2/3)*(3)=2.

Second figure: With superposition (same principle with voltage division) we have
2V*(1/2)*(1+1)=2V and 1V*(1/2)*(1+1)=1V.
Hence, Vo=3V.

You make it look so simple! Thanks for all your help, I'll try the method out with other op amp circuits!

 

[whatphysics]

That's the answers, so i guess the question was "what is Vo?" as in title of thread ?

The way that always works for opamps is this
Write KVL for voltage at opamp's + input.
Write KVL for voltage at opamp's - input.
Set them equal, solve for Vo.

1st image:
Vat +input = 2/3 , do you see why ?
Vat - input = Vo/3 , do you see why ?
equate them, 2/3 = Vo/3 ,
multiply both sides by common denominator of 3 and you get 2= Vo, swap sides to get Vo=2 .
It's that easy .

2nd image
Vat +input = 1.5 , do you see why ?
Vat - input = Vo/2 , do you see why ?
equate them, 1.5 = Vo/2
multiply both sides by 2 and you get 3= Vo, swap sides to get Vo=3 .

The KVL equations for V at + and - inputs are seldom so convenient as in the examples you gave,
but that method always works and you ought to practice until it becomes intuitive.

Thoreau didn't know he was giving electronics advice when he wrote "Simplify Simplify."

old jim

If only my teacher had been as clear as you, thank you for all your help! I'll try to solve other op amp circuits now. Thank you!