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Impedance of conductor outer surface

Definition according to Cigré guide 531 chapter 4.2.1

Symbol
$\mathscr{z}_1$
Unit
$\Omega$/m
Formulae
$\frac{m_{z,c} \rho_c}{2\pi r_{z1}} \operatorname{coth}\left(0.777m_{z,c} r_{z1}\right)+\frac{0.356\rho_c}{\pi {r_{z1}}^2}$Hyperbolic function
$\frac{m_{z,c} \rho_c}{2\pi r_{z1}} \frac{\operatorname{i0}\left(m_{z,c} r_{z1}\right)}{\operatorname{i1}\left(m_{z,c} r_{z1}\right)}$Bessel function
Related
$m_{z,c}$
Parameter m of conductor
$\pi$
Archimedes' constant $\pi$
$r_{z1}$
Radius of conductor [m]
$\rho_c$
Electrical resistivity of conductor material [$\Omega$.m]
Used in
$\mathscr{z}_{cc}$
Impedance of conductor [$\Omega$/m]
$\mathscr{z}_{int}$
Impedance internal of cable [$\Omega$/m]