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Inductance: Loop and Partial by CLAYTON R. PAUL

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5

THE CONCEPT OF “PARTIAL” INDUCTANCE

In the preceding chapters we discussed the meaning and calculation of the “loop” inductance of various conducting structures that support a closed loop of current. This “loop” inductance is calculated fundamentally for steady (dc) currents which we showed in Section 2.9 must form closed loops. If we open the loop at a point with a small gap, the loop inductance of that current loop is seen as an inductance L at these input terminals. When we pass a time-varying current around the loop via these terminals a voltage, V(t) = Ldl(t)/dt, is developed across the terminals. This voltage is essentially the Faraday’s law voltage induced into the loop. For electrically small loop dimensions, this lumped inductance and the voltage across its terminals can be represented as a lumped voltage source and placed anywhere in the loop perimeter (see Fig. 4.1). It is important, however, to remember that neither this lumped inductance nor the equivalent voltage source it represents can be placed in a unique position in the loop! This loop inductance is a property of the entire loop and its use is valid only at the input terminals of the loop. Hence, it is not possible to associate the loop inductance with any particular segment of the loop.

However, there are numerous situations, some of which were described in Chapter 1, where it is useful to develop a lumped-circuit model of a closed current loop wherein the segments of the perimeter of the loop are represented ...

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