15.1: Theory Overview

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The inductor behaves identically to the resistor in terms of series and parallel combinations. That is, the equivalent of a series connection of inductors is simply the sum of the values. For a parallel connection of inductors either the product-sum rule or the “reciprocal of the sum of the reciprocals” rule may be used. Capacitors, in contrast, behave in an opposite manner. The equivalent of a parallel grouping of capacitors is simply the sum of the capacitances while a series connection must be treated with the product-sum or reciprocal rules.

For circuit analysis in the steady state case, inductors may be treated as shorts (or for more accuracy, as a small resistance known as the coil resistance, \(R_{coil}\), which is dependent on the construction of the device) while capacitors may be treated as opens. If multiple capacitors are in series, the applied voltage will be split among them inversely to the capacitance. That is, the largest capacitors will drop the smallest voltages.