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!