Simple Nature - Light and Matter

a stylized solenoid, d, is the symbol used to represent an inductorin a circuit regardless of its actual geometry.How much energy does an inductor store? The energy density isproportional to the square of the magnetic field strength, which isin turn proportional to the current flowing through the coiled wire,so the energy stored in the inductor must be proportional to I 2 . Wewrite L/2 for the constant of proportionality, givingU L = L 2 I2 .As in the definition of capacitance, we have a factor of 1/2,which is purely a matter of definition. The quantity L is called theinductance of the inductor, and we see that its units must be joulesper ampere squared. This clumsy combination of units is morecommonly abbreviated as the henry, 1 henry = 1 J/A 2 . Ratherthan memorizing this definition, it makes more sense to derive itwhen needed from the definition of inductance. Many people knowinductors simply as “coils,” or “chokes,” and will not understandyou if you refer to an “inductor,” but they will still refer to L as the“inductance,” not the “coilance” or “chokeance!”There is a lumped circuit approximation for inductors, just likethe one for capacitors (p. 578). For a capacitor, this means assumingthat the electric fields are completely internal, so that componentsonly interact via currents that flow through wires, not due to thephysical overlapping of their fields in space. Similarly for an inductor,the lumped circuit approximation is the assumption that themagnetic fields are completely internal.Identical inductances in series example 19If two inductors are placed in series, any current that passesthrough the combined double inductor must pass through bothits parts. If we assume the lumped circuit approximation, thetwo inductors’ fields don’t interfere with each other, so the energyis doubled for a given current. Thus by the definition of inductance,the inductance is doubled as well. In general, inductancesin series add, just like resistances. The same kind of reasoningalso shows that the inductance of a solenoid is approximatelyproportional to its length, assuming the number of turns per unitlength is kept constant. (This is only approximately true, becauseputting two solenoids end-to-end causes the fields just outsidetheir mouths to overlap and add together in a complicated manner.In other words, the lumped-circuit approximation may not bevery good.)Identical capacitances in parallel example 20When two identical capacitances are placed in parallel, any chargedeposited at the terminals of the combined double capacitor willdivide itself evenly between the two parts. The electric fields sur-f / Inductances in series add.g / Capacitances in paralleladd.Section 10.5 LRC Circuits 591