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                       FIGURE 11.40  Iron-core inductor.



                       you may recall from early physics experiments with electromagnets. In an ideal inductor, the resistance
                       of the wire is zero, so that a constant current through the inductor will flow freely without causing a
                       voltage drop. In other words, the ideal inductor acts as a short circuit in the presence of DC currents. If a
                       time-varying voltage is established across the inductor, a corresponding current will result, according to
                       the following relationship:


                                                                 di L
                                                         v L t() =  L-------                    (11.36)
                                                                 dt
                       where L is called the inductance of the coil and is measured in henry (H), where

                                                       1 H =  1 V sec/A                         (11.37)

                       Henrys are reasonable units for practical inductors; millihenrys (mH) and microhenrys (µH) are also
                       used.
                         The inductor current is found by integrating the voltage across the inductor:


                                                       i L t() =  1 ∫  t  v L dt                (11.38)
                                                              ---
                                                              L  – ∞
                       If the current flowing through the inductor at time t = t 0  is known to be I 0 , with

                                                                  1
                                                         (
                                                   I 0 =  i L t = t 0 ) =  --- ∫ t 0  v L dt    (11.39)
                                                                  L  – ∞
                       then the inductor current can be found according to the equation


                                                  i L t() =  1 ∫  t  v L t +  I 0 t ≥ t 0       (11.40)
                                                               d
                                                         ---
                                                         L  t 0
                       Inductors in series add. Inductors in parallel combine according to the same rules used for resistors
                       connected in parallel. See Figs. 11.41–11.43.
                         Table 11.4 and Figs. 11.36, 11.41, and 11.43 illustrate a useful analogy between ideal electrical and
                       mechanical elements.


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