# reactance

#### bujak18

Joined Nov 12, 2008
49
what is the reactance of a .22uf, 250v capacitor at 400Hz?

#### DrNick

Joined Dec 13, 2006
110
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)

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#### studiot

Joined Nov 9, 2007
5,003
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.

#### bujak18

Joined Nov 12, 2008
49
does anyone know the exact answer? pls

#### mik3

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

#### bujak18

Joined Nov 12, 2008
49
can u simplify this? pls

#### davebee

Joined Oct 22, 2008
539
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.