reactance

Discussion in 'Homework Help' started by bujak18, Jan 14, 2009.

  1. bujak18

    Thread Starter Active Member

    Nov 12, 2008
    49
    0
    what is the reactance of a .22uf, 250v capacitor at 400Hz?
    :(
     
  2. DrNick

    Active Member

    Dec 13, 2006
    110
    2
    Are you familiar with the laplace transform? If not, here is a walk through to get the reactance of a capacitor:

    For a capacitor

    i = C * dv/dt

    Therefore,

    v = 1/C * integral(i, 0 , t) + V0.

    Now the laplace transform is defined as follows

    I(s) = integral(i(t) * exp(-s*t), 0, inf)

    Now the cool thing is, if we integrate I(t) prior to performing the laplace transform we will get

    i2(t) = integral(i(t))

    I2(s) = I(s)/s


    Applying this rule to our formula for v we get

    V(s) = 1/(C*s)*I(s).

    the reactance is just the imaginary part of the resistance of a component,
    therefore the reactance is:

    1/(C*j*2*pi*f)
     
    Last edited: Jan 14, 2009
  3. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    Whilst Santa is busy stuffing is, js and ks into next years christmas stockings it may be worth noting that the reactance is given by

    X_{c} = 1/2π f C

    i.e. = 1/(2πx400x2.2 x10^{-7}) ohms

    The voltage rating of the capacitor or the applied voltage is immaterial.
     
  4. bujak18

    Thread Starter Active Member

    Nov 12, 2008
    49
    0
    does anyone know the exact answer? pls
     
  5. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Xc=1/(2*pi*f*C)=1/(2*pi*400*0.22*10^-6)=1.8 Kohm
     
  6. bujak18

    Thread Starter Active Member

    Nov 12, 2008
    49
    0
    can u simplify this? pls
     
  7. davebee

    Well-Known Member

    Oct 22, 2008
    539
    46
    bujak18, I think that what these guys wrote is as simple as it gets.

    They took the definition of capacitive reactance, plugged in your values and gave you the answer.
     
  8. bujak18

    Thread Starter Active Member

    Nov 12, 2008
    49
    0
    nm i figured it out thanks guys my cousin was typing that hes 14 sry!
     
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