# op-amp and delta resistors

#### hgmjr

Joined Jan 28, 2005
9,029
i'm probably completely off, but would Vo=20/27 Volts?
Caramel,

It will be helpful if you can post the steps you used to arrive at the above answer. That way it will be easier to follow your line of thought in arriving at your answer.

hgmjr

#### caramel

Joined Feb 9, 2007
19
And you said, There is no simplification. The redrawn circuit is identical to the original circuit.
i do understand virtual ground, this is my second circuits course.. regarding the cricuit, i'm sorry i guess i used the wrong word.. i meant to say i'd like to see how the first circuit was re-drawn/transformed to your circuit.

but.. so far, i've re-worked the entire problem a million times.. i labeled all voltages in terms of Vs, to no avail... i keep going in circles!... no examples in book or lecture.

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#### caramel

Joined Feb 9, 2007
19
Caramel,

It will be helpful if you can post the steps you used to arrive at the above answer. That way it will be easier to follow your line of thought in arriving at your answer.

hgmjr
i reviewed it now, it's completely wrong, no use of posting it

#### hgmjr

Joined Jan 28, 2005
9,029
You have calculated the correct answer.

hgmjr

#### caramel

Joined Feb 9, 2007
19
strange.. i don't think the math was right, so i probably got the correct answer by accident. but knowing the right answer will help me work through the problem some more until i reach a legitimate route to getting that answer.

thanks

#### caramel

Joined Feb 9, 2007
19
so lets see, for Vo = 20/27 V:

eq1: Vo = Vp + 4Vs/9

and

eq2: Vp = 2Vs/3 ==> 0Vo + Vp = 2Vs/3 ==> 0Vo = -Vp + 2Vs/3

eq2/eq1 ==> Vs = 2/3 Volts

and Vo = 10Vs/9 = (10/9)(2/3) = 20/27 Volts

#### hgmjr

Joined Jan 28, 2005
9,029
so lets see, for Vo = 20/27 V:

eq1: Vo = Vp + 4Vs/9

and

eq2: Vp = 2Vs/3 ==> 0Vo + Vp = 2Vs/3 ==> 0Vo = -Vp + 2Vs/3

eq2/eq1 ==> Vs = 2/3 Volts

and Vo = 10Vs/9 = (10/9)(2/3) = 20/27 Volts
caramel,

Vo = 10/9 Vs

I'm still studying your math to see if I can figure out why you multiplied by 2/3.

hgmjr

#### caramel

Joined Feb 9, 2007
19
haha, yeah, no wonder i thought that was so strange!

right, the answer i'm 100% sure of is Vo= 10Vs/9 .. but she didn't say solve for Vo in terms of Vs, so i'm assuming she wants a number.. and that's what's been driving me crazy all along! if she had said "in terms of Vs" i would've had the problem solved quite a long time ago... i guess i'll just turn it in with 10Vs/9 as my final answer.

to answer your question, i multiplied by 2/3 later because that's what i got for Vs out of my (vudo) math... (10/9)(2/3) = 20/27

#### hgmjr

Joined Jan 28, 2005
9,029
Here is my efforts at solving the problem.

The solutions were both done using Millman's Theorem.

Solution one is a general case and solution two is the specific case.

hgmjr

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#### caramel

Joined Feb 9, 2007
19
wow! lol.. we haven't had Millman's Thm yet, but i see you got the same answer i did, so i guess all is good....... she used to always specify if she wanted us to solve using variables only, don't know why she didn't here!

anyway, thanks so much.. i really appreciate your efforts, hgmjr.. and thanks to everyone else who helped, especially Ron H for providing the easier-to-work-with circuit.. you guys/ladies are life-savers

#### Ron H

Joined Apr 14, 2005
7,014
Yep, that's the same answer I got.
Caramel, I still don't understand this statement of yours:
i'd like to see how the first circuit was re-drawn/transformed to your circuit.

#### caramel

Joined Feb 9, 2007
19
nevermind, i see what you did

#### hgmjr

Joined Jan 28, 2005
9,029
wow! lol.. we haven't had Millman's Thm yet, but i see you got the same answer i did, so i guess all is good....... she used to always specify if she wanted us to solve using variables only, don't know why she didn't here!

anyway, thanks so much.. i really appreciate your efforts, hgmjr.. and thanks to everyone else who helped, especially Ron H for providing the easier-to-work-with circuit.. you guys/ladies are life-savers
caramel,

Here is a link to the All About Circuits tutorials section on Millman's Theorem.

hgmjr