Voltage across the output resistor for this opamp circuit

[jaus tail]

Homework Statement

Find the voltage across R3

Relevant Equations

No current flows inside opamp

Here is question: Find voltage across R3
options:
10V
11V
5V
2V

Attempt: No current flows through Opamp, so 1mA flows through R3, this gives voltage across R3 = 1ma * 1K = 1V.
But that is not in option.
Where am I wrong? No current flows inside or outside opamp, right?

 

[BvU]

No current flows inside or outside opamp, right?

From - to + ! (The output currect can be considerable) !
I.e. the 1 mA flows through R2 in opposite direction wrt Vb - Va

 

[jaus tail]

1 mA will flow left to right through R1, then left to right through R2 and then top to bottom through R3. Right?

 

[BvU]

What about the opamp ? Is it passive ?

Right?

That would make Va = 11 V ? and Vb = $-\infty$ ? After all, Vb = $-$ N $\times$ Va with N a big number...

 

[jaus tail]

What does passive mean? This is the only data that is given. The diagram and the question to find Voltage across R3.

 

[LvW]

The key for solving the problem is the following:
For an ideal opamp the voltage between the inv. terminal and ground is zero. This is the result of negative feedback.
Hence, find the expression for this voltage (depends on the input current as well as the opamps output voltage Vout, use the superposition rule) and set it to zero - and solve for Vout.
It is a simple calculation...

 

[phyzguy]

Where am I wrong? No current flows inside or outside opamp, right?

No current flows into or out of the op amp inputs, but current can and does flow into or out of the op amp output. So the current through R3 is not the same as the current through R2.

 

[jaus tail]

The key for solving the problem is the following:
For an ideal opamp the voltage between the inv. terminal and ground is zero.

Does this mean Va is 0?
Or
Can i solve it like:
( 0 - Va ) / R1 = 1mA
This gives Va.
Then (Va - Vb)/R2 = 1mA. It's the same current.
This gives Vb ??

 

[phyzguy]

Does this mean Va is 0?

Yes.

Or
Can i solve it like:
( 0 - Va ) / R1 = 1mA
This gives Va.

No! You don't know what the voltage at the top of the current source is.
Edit - A better way to say it is that you can't assume that the voltage at the top of the current source is zero. You can calculate what that voltage is given that Va=0 and knowing R1 and the current.

 

[LvW]

@jaus tail - do you know the superposition rule?
There are two sources contributing to the voltage Va: The input current source and the opamps output voltage Vout. The influence of both sources on the voltage Va can be (and must be ) calculated separately!

 

[jaus tail]

Yeah I know superposition. The output voltage is like a series voltage source / battery to right or to left of b?

 

[jaus tail]

I'm confused about superposition. The opamp's output Vout is because of the input current source. So how are there two independent sources? If i consider only Vout and open circuit the current source, then Vout will be zero, cause Vout is because of Iinput.

 

[jaus tail]

is this the explanation:
using concept of virtual ground, we get that inverting terminal of opamp is at ground. 0V
so current through R2 is 1mA. No current flows into opamo.
so (Va-Vb)/R2 = (0-Vb)/R2 = 1mA
So -Vb/10k = 1mA.
This gives Vb = 10V, which is there in option.

 

[phyzguy]

is this the explanation:
using concept of virtual ground, we get that inverting terminal of opamp is at ground. 0V
so current through R2 is 1mA. No current flows into opamo.
so (Va-Vb)/R2 = (0-Vb)/R2 = 1mA
So -Vb/10k = 1mA.
This gives Vb = 10V, which is there in option.

Yes. That's all there is to it.

 

[jaus tail]

Ok. Thanks. Just for knowledge: if current is going into the output of the opamp, then where does it go from there? Like current needs a closed path.
So if current enters opamp from output, where does it come out from?
Or if current is coming out from output of opamp, how does it enter the opamp?

 

[phyzguy]

Ok. Thanks. Just for knowledge: if current is going into the output of the opamp, then where does it go from there? Like current needs a closed path.
So if current enters opamp from output, where does it come out from?
Or if current is coming out from output of opamp, how does it enter the opamp?

The op amp has connections to the power supplies, as shown in this figure. They source or sink the output current.

 

[LvW]

is this the explanation:
using concept of virtual ground, we get that inverting terminal of opamp is at ground. 0V
so current through R2 is 1mA. No current flows into opamo.
so (Va-Vb)/R2 = (0-Vb)/R2 = 1mA
So -Vb/10k = 1mA.
This gives Vb = 10V, which is there in option.

Not unimportant( the sign): Vb= - 10V.

 

[jaus tail]

Thanks for the help. I didn't use superposition though. Is there some other method to arrive at answer using superposition?

 

[LvW]

Thanks for the help. I didn't use superposition though. Is there some other method to arrive at answer using superposition?

The voltage at the inv. input is Vn=Vn1+Vn2.
(1) Vn1 caused by I1 only (for Vout=Vb=0): Vn1=I1*R2=10V.
(2) Vn2 caused by Vout=Vb only (for I1=0, open circuit): Vn2=Vout=Vb (no voltage drop across R2).
(3) Vn=Vn1+Vn2=10V+Vb=0
(4) therefore, Vb=-10V.