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?
- 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)