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When dealing with inductors Sears & Zemansky state that "we need to develop a general principle analogous to Kirchhoff's loop rule". With an inductor present in the circuit they state that there is a non-conservative electric field within the coils $\vec E_n$ as well a conservative electric field $\vec E_c$. Assuming that the inductor has negligible ...

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The real part of the impedance $Z_{aa'}$ is resistive so all you need to decide as to what component, inductor or capacitor, you would assign a negative imaginary part to. Perhaps do it by a process of elimination or write down the general formulae for the reactances of capacitors and inductors?

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Just like the curiousone told you, since the curl of E is not zero, you're dealing with a non-conservative field. So if you consider the potential difference to be the work done by E to get from the point P to Q it does matter the way you take. Griffiths answer is based on the trajectory to go from P to Q in a straight line.

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