A coil has self-inductance and a winding of resistance

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

Electricity, Magnetism and Electromagnetism, Ch Self and mutual inductance and magnetic field energy

Problem

A coil has self-inductance

L = 0.25\ \mathrm{H}

and a winding of resistance

R = 3.0\ \Omega

. Starting from zero current, a supply with an adjustable rheostat is used to raise the current in the coil at the uniform rate

20\ \mathrm{A\,s^{-1}}

, so that after

0.20\ \mathrm{s}

the current is

4.0\ \mathrm{A}

. Assume

L

and

R

are constant and that no energy leaves the coil except as Joule heat in its own winding. A student says: "The supply delivered

\tfrac12 LI^2

in total, because that is the energy the coil ends up with." ((a)) Find the energy stored in the coil's magnetic field at the end of the

0.20\ \mathrm{s}

. ((b)) Find the Joule heat produced in the winding during the same

0.20\ \mathrm{s}

. ((c)) Hence find the total electrical energy the supply delivered to the coil, and say where the quoted claim went wrong.

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