Hello, I have a very beginner-like question.

How should I know what is the direction of current through resistors? For example, current I is here shown as current that goes from node 3 to node 4. Can I do the with the same current that goes from 4 to 3 or there is some rule that I don't know?

Sorry for disturbing with such a question, but I am a bit confused. Thanks in advance.

 

When you are doing current loop analysis you simply pick a direction and stick with it.
If your analysis results in a negative value, then the current goes in the opposite direction.

 

Yes, understood.
But, in this problem, do we have only one current I that goes from Vo to the ground (behind R4) or we have many currents?
For example, from node 3 one part goes to node 4 and the other part goes towards the node 1?

*Op amps are ideal.

 

As the op-amps are ideal, the current from node 1 to node 3 must be equal to the current from node 3 to node 4 and likewise equal to the current from node 4 to node 2.

 

As the op-amps are ideal, the current from node 1 to node 3 must be equal to the current from node 3 to node 4 and likewise equal to the current from node 4 to node 2.

All right, so it means that the current through R4 (between nodes 7 and 5) is the same as through R1 -> the current I?

 

Yes, understood.
But, in this problem, do we have only one current I that goes from Vo to the ground (behind R4) or we have many currents?
For example, from node 3 one part goes to node 4 and the other part goes towards the node 1?

*Op amps are ideal.

No, the current flowing from Vo back through R4 is not necessarily the same current that flows through R1. The reason is that R2 and R3 are NOT in series -- the opamp output is connected to the same nodes as R2 and R3. The same on the bottom part of the circuit. Those opamps supply whatever current, positive or negative, is required to hold V3 = Vi1 and V4 = Vi2. Remove one or both R3 resistors and that will still be the case.

 

If it is not too much, how did they get the answer:


Where V2 and V1 are voltages in nodes 2 and 1 respectively.

Also, do you know whether there is a some good book of similar problems to this for practice?

 

No, the current flowing from Vo back through R4 is not necessarily the same current that flows through R1. The reason is that R2 and R3 are NOT in series -- the opamp output is connected to the same nodes as R2 and R3. The same on the bottom part of the circuit. Those opamps supply whatever current, positive or negative, is required to hold V3 = Vi1 and V4 = Vi2. Remove one or both R3 resistors and that will still be the case.

If I got You right, the currents should look like this? Id and Ib are the same?

 

What is the voltage at Node 3?

What is the voltage at Node 4?

What is the voltage across R1?

What is I?

What is the current through the bottom R2?

What is the voltage across the bottom R2?

What is the voltage at Node 2?

What is the current through the bottom R3/R4?

What is the voltage at Node 6?

What is the voltage at Nod5?

What is the current through the top R2?

What is the voltage across the top R2?

What is the voltage at Node 1?

What is the voltage across the top R3?

What is the current in the top R3?

What is the current in the top R4?

What is the voltage at Node 7?

What is Vo?

What is Vo in terms of (Vi2 - Vi1)?

 

If I got You right, the currents should look like this? Id and Ib are the same?

Yes.

 

What is the voltage at Node 3?

What is the voltage at Node 4?

What is the voltage across R1?

What is I?

What is the current through the bottom R2?

What is the voltage across the bottom R2?

What is the voltage at Node 2?

What is the current through the bottom R3/R4?

What is the voltage at Node 6?

What is the voltage at Nod5?

What is the current through the top R2?

What is the voltage across the top R2?

What is the voltage at Node 1?

What is the voltage across the top R3?

What is the current in the top R3?

What is the current in the top R4?

What is the voltage at Node 7?

What is Vo?

What is Vo in terms of (Vi2 - Vi1)?

Voltage at Node 3 is Vi1.
Voltage at Node 4 is Vi2.
Voltage across R1 is Vi1-Vi2.
I is (Vi1-Vi2)/R1.
Voltage in Node 2 is V2 = Vi2 - R2 * I.

What is the current through the bottom R3/R4? Ic = V2/(R3+R4)?
What is the voltage at Node 6? V6 = V2*R4 / (R3+R4), maybe? I.e. V6 = R4 * Ic.

Voltage in Node 5 is the same as in Node 6; V5=V6.

Current across the top R3: Ib = (V1 - V5) / R3?

Id = Ib

Voltage at Node 7: V7 = V5 - R4 * Ib.

Right?

 

Looks good. Now just bring it all together. It might help to write each step along the way in terms of Vi1 and Vi2.

 

Thank you very much. Sorry for all trouble.

Just to make it clear for myself - When there is an op-amp output connected to some node - there is an extra current through it and because of that currents through R2 and R3 cannot be the same?

 

Thank you very much. Sorry for all trouble.

Just to make it clear for myself - When there is an op-amp output connected to some node - there is an extra current through it and because of that currents through R2 and R3 cannot be the same?

You only know that they MAY not be the same. They don't HAVE to be the same. It's always possible that the opamp just happens to not be sourcing or sinking any current and, if that's the case, then the currents WILL be the same.

This is absolutely no different from any other situation in which more than two components are connected to the same node. The current in any two of them may or may not be the same.

 

Yes, yes, of course. I did not say it well.

I can't be more grateful. Thanks, WBahn! You always explain so good.