# formula for impedance

Discussion in 'General Electronics Discussion' started by kbcheong, May 3, 2012.

1. ### kbcheong

25
0
Mar 24, 2012
I come accross the impedance for an inductor an capacitor combined is Z = XL - XC, for a resistor and capacitor in series is Z = sqrt(R^2 + XC^2) and how do you obtain a formula for a combination of a capacitor, an inductor and a resistor in series and in parallel?

2. ### Harald KappModeratorModerator

11,307
2,588
Nov 17, 2011
Treat the capacitor and the inductor as resistors with impedance Xc and Xl, respectively. Use the standard way of calculating series resistors or parallel resistors inserting Xc and Xl instead of R.

This
doesn't look right. What do you mean by "combined"? In what manner combined?

Harald

3. ### john monks

693
2
Mar 9, 2012
The formula Z=XL-XC is correct for a series circuit. The formula for a parallel circuit involving a capacitor, an inductor and a resistor is 1/(1/XC+1/XL+1/R). This can be a nasty equation to deal with because it involves imaginary numbers. Get a good math book to learn to deal with imaginary numbers. It's not very hard. The formula for a series is XC+XL+R. Your XL reactance leads the reactance of the XC by 180 degrees so you will have to subtract one from the other like you did before. The R has no phase shift. So what you will end up doing trigonometry to solve the problem. So get a math book with electronics circuits to see how the math works. What I find with most electronics and physics students is that the math is not the hard part. It is the physics. You need to fully understand what an inductor and capacitor is and how it works. The resistor is easy enough. Then the math will make perfect sense.

4. ### Harald KappModeratorModerator

11,307
2,588
Nov 17, 2011
Why would
be correct? You used the right principle for the parallel circuit, why not for the series circuit?

If you treat XL and Xc as complex resistors (aka impedance) then Z=XL+XC.
Take the special case Z=0. This gives only a meaningful result for Z=XL+XC where C=1/(w^2*L). This is called series resonance and Z is only limited by parasitic effects (wire resistance etc).
With Z=XL-XC you don't get any meaningful result.

Harald

5. ### timothy48342

218
1
Nov 28, 2011
For series inductor and capacitor:

Z = XL + XC

However XC (capacitive reactance) is considered to be in the negative imaginary direction. (-j)

XL = j w L

XC = -j 1/( w C)

Z = [w L - 1/(w C) ] j

I think its that minus is the last formula that causes some confusion sometimes. People stick it the first formula instead.

--tim

6. ### Harald KappModeratorModerator

11,307
2,588
Nov 17, 2011
Both impedances, for inductor and for capacitor, are imaginary. The difference is the phase angle.
Writing Xc = -j * 1/(wC) is just a mathematical transformation of Xc = 1/j(wC) but still the impedance is positive and non-zero.

While your math is correct, I think the way I put it is more common.

Our common problem is that neither of us stated the equations for Xl and Xc in the first place so we talked at cross purposes while thinking we were on same terms. Timothy's explanation helped us untangle the knot.

Harald

Last edited: May 5, 2012