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
    20,221
    5,747
    You have I1 and I3, right? What the relationship between I1, I2, and I3?
     
  4. MrAl

    Distinguished Member

    Jun 17, 2014
    3,721
    789
    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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