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Capacitive Reactance

  1. Oct 4, 2015 #1
    Hi,

    A pure capacitor C is in an a.c. circuit.

    Vc = V0 * sin(w*t)
    Q = C * Vc
    = C * V0 * sin(w*t)
    I = dQ/dt
    = wCV0 sin(wt)
    then I0 = wCV0
    Xc = V0 / I0 = 1/(wC)

    So why people would say V = I * Xc?

    Is it a must to include complex number?
     
    Last edited: Oct 4, 2015
  2. jcsd
  3. Oct 4, 2015 #2
    The derivative of sin is cos.

    You don't need complex numbers.
     
  4. Oct 5, 2015 #3
    Whoops!
    I = I0 cos(wt)
    Then V = I * Xc * tan(wt)
    not V = I * Xc
     
  5. Oct 5, 2015 #4
    The relationship V=I*Xc (with real numbers) is between the amplitudes or rms values and not between instantaneous values.
    Otherwise you need to consider Xc as a complex number, to take into account the phase difference between v and i.
     
  6. Oct 17, 2015 #5
    But why do we introduce imaginary root in it?
    Is it used to describe the phase based on the e^(i*theta)?
     
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