AC Components and Circuits Inductance
Section 15 Total Inductance Inductors in Series and Parallel The total inductance of series and parallel inductor circuits is found by using the same form of equations you've been using for series and parallel resistor circuits. Inductors in Series L_{T} = L_{1} + L_{2} + L_{3}  Inductors in Parallel L_{T} =  1  1  +  1  +  1    L_{1}  L_{2}  L_{3}    Equations Total Inductance of a Series Circuit L_{T} = L_{1} + L_{2} + L_{3} + ... + L_{n} Total Inductance of a Parallel Circuit L_{T} =  1  1  +  1  +  1  + ... +  1  L_{1}  L_{2}  L_{3}  L_{n}  Where  L_{T} = Total inductance of the series circuit
 L_{1}, L_{2}, L_{3}, L_{n} = Inductance of all the individual resistors
 The productoversum technique that is commonly used for pairs of parallel resistors works equally well for pairs of inductors. L_{T} =  L_{1}L_{2}   L_{1} + L_{2}  The shorthand notation for this equation is also to the resistance counterpart: L_{T} = L_{1}  L_{2} Example Problem Use the productoversum equation to find the total inductance of a parallel circuit comprised of inductors of 12mH and 22mH. Procedure 1. Cite the appropriate equation: L_{T} =  L_{1}L_{2}   L_{1} + L_{2}  2. Substitute the given values and do the math L_{T} =  (12 x 10^{3})(22 x 10^{3})  = 7.76 x 10^{3}  (12 x 10^{3}) + (22 x 10^{3}  Solution L_{T} = 7.6 mH  Examples Endless Examples & Exercises Given the values for inductors in series or parallel circuits, calculate the total capacitance. Work these exercises until you are confident you have mastered the procedures. Note: The answers shown in these example often do not appear in normalized forms. For example, an answer appears as 1200mH when it should be 1.2H.   Combination Inductor Circuits Inductors in SeriesParallel CombinationL_{T} = L_{1} + (L_{2}  L_{3})  Inductors in ParallelSeries CombinationL_{T} = L_{1}  (L_{2} + L_{3})  The procedures for calculating the total inductance of combination inductor circuits is identical to those for combination resistor circuits. So a few exercises should be sufficient for mastering this particular topic. Endless Examples & Exercises Given the values of the inductors in a combination circuit, calculate the total inductance. Work these examples until you are certain you understand the procedures.  
