Problem 10-3Suppose there are three inductors, each with a value of 40 µH, connected in parallelwith no mutual inductance, as shown in Fig. 10-4. What is the net inductance of the set?Interaction among inductors18710-4Inductors in parallel.Call the inductances L140µH, L240µH, and L340µH. Use the formulaabove to obtain 1/L1/401/401/403/400.075. Then L1/0.07513.333µH.This should be rounded off to 13 µH, because the original inductances are specified toonly two significant digits.Problem 10-4Imagine that there are four inductors in parallel, with no mutual inductance. Their val-ues are L175 mH, L240 mH, L3333µH, and L47.0 H. What is the total net inductance?You can use henrys, millihenrys, or microhenrys as the standard units in this prob-lem. Suppose you decide to use henrys. Then L10.075 H, L20.040 H, L30.000333H, and L47.0 H. Use the above formula to obtain 1/L13.332530030.1433041.473. The reciprocal of this is the inductance L0.00032879 H328.79µH. Thiscan be rounded off to 330 µH because of significant-digits considerations.This is just about the same as the 333-µH inductor alone. In real life, you could haveonly the single 333-µH inductor in this circuit, and the inductance would be essentiallythe same as with all four inductors.If there are several inductors in parallel, and one of them has a value that is farsmaller than the values of all the others, then the total inductance is just a little smallerthan the value of the smallest inductor.Interaction among inductorsIn practical electrical circuits, there is almost always some mutual inductance betweenor among coils when they are wound in a cylindrical shape. The magnetic fields extendsignificantly outside solenoidal coils, and mutual effects are almost inevitable. The sameis true between and among lengths of wire, especially at very-high, ultra-high, and mi-crowave radio frequencies. Sometimes, mutual inductance is all right, and doesn’t havea detrimental effect on the behavior of a circuit. But it can be a bad thing.