An air-cored solenoid is wound with turns over a length and has cross-sectional area

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic induction and alternating-current circuits · Electromagnetic induction and alternating-current circuits

Electricity, Magnetism and Electromagnetism, Ch AC circuits: phasors, complex impedance, resonance and power

Problem

An air-cored solenoid is wound with

N = 400

turns over a length

l = 0.25\,\mathrm{m}

and has cross-sectional area

A = 4.0\times10^{-4}\,\mathrm{m^2}

. It is long compared with its diameter, so the long-solenoid result for self-inductance may be used, and the resistance of its own wire is negligible. ((a)) Find the self-inductance of the solenoid. ((b)) Find its reactance at

5.0\,\mathrm{kHz}

. ((c)) The coil is now placed in series with a capacitor

C = 0.10\,\mu\mathrm{F}

(negligible leakage) and a resistor

R = 3.0\,\Omega

. Find the resonant frequency

f_0

and the quality factor

Q_{\mathrm{f}}

. ((d)) The series circuit is driven at

f_0

by an ideal sinusoidal source of amplitude

1.2\,\mathrm{V}

and negligible internal impedance. Find the rms current and the mean power delivered.

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