Calculating Unknown Voltages on Op Amp Circuits

[j172]

Hi everybody!

This is my first post as I am needing some help in a question I am struggling with. Not looking for answers, just some guidance in the right direction.

Homework Statement

[/B]
I need to calculate the unknown, highlighted, voltages on the op amp circuits (attached).

Assume all op-amps are ideal

Homework Equations

See below

The Attempt at a Solution

I have done the following so far:

a) Inverting
A=-Rf/Ri =(-100)/10=-10
Vi =I1*R1 =0.00001*100000=1 V
Vo=(-Rf/Ri )*Vi
Vo =1*-10
Vo =-10 V

b) Summing
Vo=-(Rf/R_1 V_1+Rf/R_2 V_2 )
-2=(Rf/R_1 1+Rf/(R/2) V_2 )

c) Non-inverting
V1 =V2
V1 =100 mV
V2 =100 mV

d) Current to Voltage
Vo=-I1*Rf
Vo =-0.0002*10000=-2
Vo =-2 V

I am struggling the (b). I can't see how to calculate given only one value, and also with (c)

Many thanks in advance, happy to discuss the methods.

Joel

 

[.Scott]

For A, Note that the voltage at both inputs to the op amp are equal, and at ground.
For B, I have 1R-2R+x(R/2)=0
For C & D, we agree.

 

[rude man]

a) Inverting
A=-Rf/Ri =(-100)/10=-10
Vi =I1*R1 =0.00001*100000=1 V

You have R1 wrong.

b) Summing
Vo=-(Rf/R V_1+Rf/R_2 V_2 )
-2=(Rf/R 1+Rf/(R/2) V_2 )

correct (I took out the "Rf" , should be just "R" everywhere)

c) Non-inverting
V1 =V2
V1 =100 mV
V2 =100 mV

Right.

d) Current to Voltage
Vo=-I1*Rf
Vo =-0.0002*10000=-2
Vo =-2 V

Right

I am struggling the (b). I can't see how to calculate given only one value, and also with (c)

The R's cancel. There is nothing more to do with (c) than you have already done.

 

[j172]

Thank you very much for your help

 

[rob1985]

b) Summing
Vo=-(R/R*V_1+R/R*V_2 )
-2=(R/R*1+R/(R/2)*V_2 )

So is there another step to this because this equation doesn't give V_2. do you transpose it ?

 

[rude man]

b) Summing
-2=(R/R*1+R/(R/2)*V_2 )
So is there another step to this because this equation doesn't give V_2. do you transpose it ?

It doesn't?

 

[rob1985]

can you elaborate please

 

[rude man]

can you elaborate please

Well let's see - you have one equation with 1 unknown.
If this is difficult I really am at a loss as to what to hint next, so I must perforce cease from further such.

 

[rob1985]

b is 1/2 volt

 

[NascentOxygen]

b is 1/2 volt

As a check, substitute your answer into the original equation to ensure that your answer does indeed make both sides of the equation equal.