A toroidal coil of turns is wound on a non-magnetic core of mean radius and…

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

A toroidal coil of

N = 600

turns is wound on a non-magnetic core of mean radius

r = 5.0\,\mathrm{cm}

and cross-sectional area

A = 1.0\,\mathrm{cm^2}

. The core's cross-section is small compared with

r

, so the field may be taken as uniform over it and the Chapter 12 toroid result used. The winding's own resistance is negligible. ((a)) Find the self-inductance of the toroid. ((b)) A capacitor

C = 470\,\mathrm{pF}

of negligible leakage is connected in series with it. Find the resonant frequency

f_0

and the common magnitude of the two reactances at that frequency. ((c)) A resistor

R = 8.0\,\Omega

is also in series. Find the quality factor and the half-power bandwidth in hertz. ((d)) The circuit is driven at

f_0

by an ideal sinusoidal source of amplitude

0.10\,\mathrm{V}

. Find the rms current and the mean power delivered.

Browse the problem library