
Impedance equation
Hi guys,
i need some help please with the following equation, I need to make c the subject of z=sqrt(r^2 + (xl  xc)^2).
My first step was remove the sqrt to become z^2=r^2 + (xl  xc)^2
Then expand the brackets so z^2=r^2 + (xl  Xc)(Xl Xc)
then Multiply out the brackets so z^2 = r^2 + xl^2  xc^2  2xlxc
then I'm a bit stuck where to go from there. I could move the r^2 to the other side but I'm still none the wiser on getting c as the subject.
i was also given xl= 2(pi)fl and xc = 1/ 2(pi)FC
z=104ohms r=100ohms f=50hz, l= 0.1 henry
any enlightenment would be greatly appreciated!
thanks
kris

Re: Impedance equation
$\displaystyle z^2 = r^2 + (x_L  x_C)^2$
$\displaystyle z^2  r^2 = (x_L  x_C)^2$
$\displaystyle \sqrt{z^2  r^2} = x_L  x_C$
if $\displaystyle x_L > x_C$ ...
$\displaystyle \sqrt{z^2  r^2} = x_L  x_C$
$\displaystyle x_C = x_L  \sqrt{z^2r^2}$
if $\displaystyle x_L < x_C$ ...
$\displaystyle \sqrt{z^2  r^2} = (x_L  x_C)$
$\displaystyle x_C = x_L + \sqrt{z^2r^2}$
finally ...
$\displaystyle x_C = \frac{1}{2\pi f C}$
$\displaystyle C = \frac{1}{2\pi f x_C}$

Re: Impedance equation
Hi skeeter
Thanks for the input but how do I transpose so C is the subject? Both of the above still with have xc or a c on the both sides. Sorry for not understanding and I'm sure you correct it's just that I still don to now how to use the formula by your solution :)
Thanks,
Kris.

Re: Impedance equation
Ok I get how c equals that now but the question I've been given is calculated the value of c, but how is the value of c supposed t o be calculated if I'm only given z=104 ohms, R= 100 ohms, f = 50 hz, l = 0.1 Henry. It's just throwing me as I can input the values but I still don't know xc.
thanks

Re: Impedance equation