Can someone explain to me why Vo = -1. in a short way and direct to the points, the op amp is ideal.

 

If the Op-Amp is "Ideal", then the Resistors do not enter into the equation.

An "Idea-Op-Amp" is nothing more, or less than, a Mathematical-Equation.
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The 2 kΩ resistor at the output is not relevant.
The 10 kΩ from the output to the inverting input provides negative feedback. The value of the resistor is irrelevant.

The op amp will reach one of three states, the output will reach one of the supply voltages, positive or negative supply rail (op amp is saturated), or the voltage at the inverting input must be the same as the voltage of the non-inverting input.

What must the output voltage be for the two inputs to be at the same voltage?

 

Are you familiar that in an ideal opamp, the voltage difference between the inverting and non inverting inputs MUST BE zero when the opamp is operating linearly?
As such, what output voltage would satisfy this requirement?
Exactly! Vo = -1

 

Are you familiar that in an ideal opamp, the voltage difference between the inverting and non inverting inputs MUST BE zero when the opamp is operating linearly?
As such, what output voltage would satisfy this requirement?
Exactly! Vo = -1

I dont understand, op amp senses the difference between 2 input voltages and multiply with gain then have voltage output? right? how can it be -1 this case? Can you explain shortly and direct to the point with equations

 

An ideal op amp has a voltage gain equal to infinity.

Hence any voltage difference between the inverting input and the non-inverting input would result in infinite output voltage, only limited by the power supply voltage.

The analysis should be obvious. Apply Kirchhoff Voltage Law to the negative feedback loop. We cannot do all the thinking for you.

 

how can it be -1 this case?

Redo your math.
When the output is -1V, the voltage between the two inputs is zero.

 

I dont understand, op amp senses the difference between 2 input voltages and multiply with gain then have voltage output? right? how can it be -1 this case? Can you explain shortly and direct to the point with equations

How can it be anything OTHER than -1 V?

As you've stated, the output of the opamp, if it is in its linear region of operation, is

Vo = K(Vp - Vn)

What is Vp, the voltage at the non-inverting input?

What is Vn, the voltage at the inverting input?

Then do the math -- show your work and we can help you see how the result is that Vo approaches -1 V as the opamp gain goes to infinity.

 

How can it be anything OTHER than -1 V?

As you've stated, the output of the opamp, if it is in its linear region of operation, is

Vo = K(Vp - Vn)

What is Vp, the voltage at the non-inverting input?

What is Vn, the voltage at the inverting input?

Then do the math -- show your work and we can help you see how the result is that Vo approaches -1 V as the opamp gain goes to infinity.

Here are my calculation as per your guiding equation.
View attachment 1735522001085.jpeg

 

Are you familiar that in an ideal opamp, the voltage difference between the inverting and non inverting inputs MUST BE zero when the opamp is operating linearly?
As such, what output voltage would satisfy this requirement?
Exactly! Vo = -1

is this equation correct?, then Vo= -K, K is gain
View attachment 1735522402090.jpeg

 

For an ideal op amp, the open loop gain is infinity.
What you have written makes no sense.

NOTE: The voltage at the inverting input must be equal to the voltage at the non-inverting input.
In other words (Vp - Vn) = 0.

Here is a hint: Vp = +1 V.

 

For an ideal op amp, the open loop gain is infinity.
What you have written makes no sense.

NOTE: The voltage at the inverting input must be equal to the voltage at the non-inverting input.
In other words (Vp - Vn) = 0.

Here is a hint: Vp = +1 V.

Can you read #8 from Mr @WBahn again, I follow his equation, Vo= K(Vp-Vn), Vp is voltage at non inverting terminal = 1, Vn is voltage at inverting terminal = 2. oh, you mean Vn here not 2V, I thought 2 VDC connect to inverting terminal then it is 2V.

 

I will repeat this because you are not getting it.

(Vp - Vn) = 0
Vp = +1 V

What is Vn?

 

I will repeat this because you are not getting it.

(Vp - Vn) = 0
Vp = +1 V

What is Vn?

okay, Vn = +1

 

okay, Vn = +1

Correct.
Now, what is Vo?

 

Correct.
Now, what is Vo?

You mean this???

 

You've got it!

 

You've got it!

How about this pic, this pic shows V2 and V1 means they are different, then take V2-V1 and multiply with A gain then have Output voltage., compared to the problem , V2 = 1, V1 = 2, then V2-V1 = -1, is somewhere wrong??

 

In that picture, A = ∞.

 

In that picture, A = ∞.

and in the problem is the same, right? Why Cannot apply the definition of Op amp like the picture I just added? is something different between the problem and the Definition circuit in the picture I just added?