# Finding total impendence of an inductor?

I want to find the total impendance of a coil. I think I know how to do it but I'm not sure.

Z = X + R

X = 2(pi)wL

L = (uAN^2)/l

Z is impendance, R is resistance of the wire of the coil, X is the reactance, w is current frequency in hertz, L is inductance, u is permeability of the core, A is area of the coil loops, N is number of turns in coil, and l is the length of the coil.

Together this would yield

Z = (2(pi)wuAN^2)/l + R

Would this be correct?

### 1 Answer

- EckoLv 76 years agoFavorite Answer
All these formulas only apply to a sine wave = single frequency.

Z is from ohms law if you have measured V and I:

Z + V/I

Ideally Z is stated as a vector |Z|, which means a magnitude in ohms and a phase angle in degrees.

If X and R are known:

Z + sqrt(R^2 + X^2). This is using trigonometry to account for the resulting direction of the vector (phase angle) of the two components R and X.

Some calculations involving power, voltage, impedance and current are easier using vectors and trigonometry, while others are easier using complex numbers (real and imaginary component). Complex numbers have a set of rules for arithmetic using them. Adding them as for two impedances in series is very straight forward.

Z as a complex number is R + jX

The following formulas allow for converting from one representation to the other.

PF (Power factor) = true power / apparent power = cos(θ) from trig.

θ = arccos(PF)

|Z| = V / I with a phase angle (θ)

Rseries = |Z| cos(θ)

Xseries = |Z| sin(θ)

Z = R + jX

|Z| = sqrt(R^2 + X^2) where X is the net reactance of XL and Xc.

θ = arctan(Xs / Rs)