Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / Section A / 4 / Solution

To find the magnitude uncertainty of a series RL impedance, put $X=\omega L$. Then $z=|Z|=\sqrt{R^2+X^2}=168.003\Omega$ andIf the quoted errors are independent standard uncertainties, ${\sigma }_R=1\Omega$ and ${\sigma }_X=6\Omega$ giveIf they denote strict bounds instead, the first-order bound is $(R\Delta R+X\Delta X)/z=5.42\Omega$. The source does not specify their statistical interpretation, so these two error conventions should not be conflated.