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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

  • Ecko
    Lv 7
    6 years ago
    Favorite 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)

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