= Magnitude uncertainty of a series RL impedance
{title2=$\sigma_z^2=(R^2\sigma_R^2+X^2\sigma_X^2)/z^2$}
For $z=\sqrt{R^2+X^2}$ with <reactance> $X=\omega L$, linear differentiation gives $dz=(R\,dR+X\,dX)/z$. <Independent> <standard uncertainties> give the title formula; correlated inputs add $2RX\operatorname{Cov}(R,X)/z^2$. Hard error bounds instead add absolute linear contributions. The meaning of an error bar is an additional measurement assumption, not a consequence of the impedance formula.
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