Circuit with OP Amp and capacitors. Help finding U

Discussion in 'Homework Help' started by John Di, Jan 15, 2015.

  1. John Di

    Thread Starter New Member

    Jan 15, 2015
    3
    0
    DSC_0036.JPG [​IMG]
    Can someone please help me find expressions for i2, i3 and i5?
    I know i1 must be Vin-Vx/R1.
    i3 is theoretically Vx-Vout/R2, but im stuck at i5 and i2.
    Thank you very much.
     
  2. dalam

    Member

    Aug 9, 2014
    58
    6
    I5 = Vout/Xc1
    I2=(Vx-Vout)/Xc2
    Its upto you how do you define Xc. You can define it using S (laplace) or using complex variables.
     
  3. WBahn

    Moderator

    Mar 31, 2012
    17,716
    4,788
    You have I1 and I3, right? What the relationship between I1, I2, and I3?
     
  4. MrAl

    Well-Known Member

    Jun 17, 2014
    2,421
    488
    Hi,

    As others have pointed out, the only difference between a resistor and capacitor in calculating the current is the capacitor has a complex impedance while the resistor has just a real impedance which is called the resistance. This means we have to use complex numbers to calculate the current.

    For the resistor we have:
    i=v/R

    and for the cap we have:
    i=v/Z

    where Z is the complex impedance:
    Z=1/(j*w*C)

    and j is the imaginary operator and w is the angular frequency equal to 2*pi*f with f the frequency in Hertz.

    This is sometimes shortened to:
    Z=1/(s*C)

    where s=j*w.

    So if we assume you know the voltage across the cap is v then we have:
    i=v/z=v/(1/(s*C))

    and using algebra:
    i=v*s*C/1=v*s*C

    and since s=j*w we end up with:
    i=v*j*w*C.

    This is purely imaginary which means the current is 90 degrees out of phase with the voltage.

    You have to be a little careful though because here we use the impedance not the reactance. Impedance is usually represented with a Z while reactance is usually represented with an X. If we try to use reactance instead of impedance we end up with a real quantity and that is not entirely correct.
     
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