A real coil is not an ideal inductor

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Foundations of mathematical language

Mathematical Methods for Physics, Ch Complex numbers, the complex exponential and phasors

Problem

A real coil is not an ideal inductor, because its winding has resistance. Model it as an ideal resistor

R_{\mathrm w}

in series with an ideal coil

L_{\mathrm c}

. Connected alone across a supply of

10.0\,\mathrm{V}

peak at

50\,\mathrm{Hz}

, it draws a current of

0.200\,\mathrm{A}

peak that lags the supply by

1.20\,\mathrm{rad}

. ((a)) Find

R_{\mathrm w}

and

L_{\mathrm c}

. ((b)) A classmate says the same measurement could equally come from a resistor in series with a capacitor. Decide, using the sign of the imaginary part of the impedance under this chapter's

e^{-i\omega t}

convention. ((c)) Find the mean power the coil takes from the supply, in two ways.

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