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Ideal Op-Amp

  1. Oct 31, 2016 #1
    1. The problem statement, all variables and given/known data
    f89f253e8d.jpg

    2. Relevant equations

    KCL
    I = V/R
    V+ = V- (ideal op amp)


    3. The attempt at a solution

    d620e6cb77.jpg

    I really don't think my voltages for ia and ib are correct. Im just not sure how to use the V- = 4V in those some how?
     
  2. jcsd
  3. Oct 31, 2016 #2

    Charles Link

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    The ## V_- ## terminal is equal to ## V_+=+4V ##. The three current sources feed into (or draw current from) the feedback resistor and feed through the feedback resistor. No current goes across the infinite input impedance. The output voltage is determined by the voltage drop through the feedback resistor. Any necessary additional output current out of the op-amp will be supplied through the load resistor (or extra current from the feedback resistor will go into the output pin) to make the voltage drop across the load resistor equal the voltage drop from the output pin of the op-amp to ground. (The output pin of the op-amp has its voltage determined by the ## V_- ## virtual ground and the feedback loop, and can supply extra current to the load resistor freely as needed, with basically an infinite supply.) ## \\ ## Note: Your equation should read ## i_d=i_a+i_b+i_c ##. (## i_b ## and ## i_c ## are both negative but the equation still reads how I just gave it.)
     
    Last edited: Oct 31, 2016
  4. Oct 31, 2016 #3
    Hm. I understand the KCL equation you gave. At the moment my issue is relating to filling in that KCL equation with values.

    id = ia +ib + ic

    Ia = 16/16000? Is that correct? My question is do I have to take the V- into account when calculating the currents for Ia and Ib. I know I have to use it for Ic.
    I keep having trouble with voltages in op-amps related circuits. I've tried going over them and reviewing KCL and the basics but theres always a different sort of "trick" in each question with voltages.
     
  5. Oct 31, 2016 #4

    Charles Link

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    Meanwhile to compute ## i_c ##, ## i_c=(-5-4)V/(12 \, k \Omega)=-.75 mA ##. The others should be easy to compute in a similar manner. And yes, you need to use the ## V_-=4V ## in those as well. Note: ## i_d ## should be fairly easy to compute. Once you have that, you can determine ## V_o ##.
     
    Last edited: Oct 31, 2016
  6. Oct 31, 2016 #5
    Is this correct?

    70b13cc839.jpg

    One more question. In calculating ia and ib, my intuition tells me that it should be (16V - Voltage at A)/16000 and (2V- Voltage at A)/8000. However we are using -4V instead. Is the entire vertical line which contains A a single node? If so shouldn't the node voltage at A be 4V as well?

    This is what my intuition tells me: V = eb - ea for the voltage across 16k resistor
    89199d99c4.jpg
     
  7. Oct 31, 2016 #6

    Charles Link

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    You could say ## i_d=-.25 mA ##, but yes your -1/4000 is correct. What do you get for ## V_o ##? (That should be easy to get.) Your -6V voltage drop is correct. Suggest you write out the algebraic result to solve for ## V_o ##. If you consider ## V_o ## as generating a positive +.25mA current back through the feedback resistor, it might be easier to compute.
     
  8. Oct 31, 2016 #7
    I think you apply current division to get V0:

    e9721f3169.png = current through 12k resistor.
    That turns out to be -1/6000.

    V = IR
    V = (-1/6000) x (12000)
    V = -2V

    which.. isnt the right answer. The answer given to us is 10V
     
  9. Oct 31, 2016 #8

    Charles Link

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    The full algebra is ## 4-V_o=-6 ##. Thereby ## V_o=10 \, V ##. Alternatively, you could write ## V_o-(.25mA)(24k \Omega)=4V ##
     
  10. Oct 31, 2016 #9
    Where are you getting the 4 from?
     
  11. Oct 31, 2016 #10

    Charles Link

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    ## 4V=V_- ## which is also point "A". Your diagram is probably confusing you slightly, but these 3 currents(considering them as positive) feed into ## V_- ## And they can't go inside the op-amp because the input impedance is infinite. The current has nowhere else to go but through the feedback resistor.
     
  12. Oct 31, 2016 #11

    Charles Link

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    @CoolDude420 Please read the edited version of post #10 above.
     
  13. Oct 31, 2016 #12
    Ah so the 4V at point A plus the 6V drop across the 24k resistor gives 10V node voltage at the point to the right of i0. And that 10V is between The 13k resistor and ground so 10v across that resistor.

    Perfect. I got the right answer for part b too. Awesome. thank you so much!!!!!!!!!!!!
     
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