Three inductors are arranged in series in one case and in parallel in another ca

Question

Three inductors are arranged in series in one case and in parallel in another case (see next page). The voltage difference between points A and B is V. Determine an expression for the inductance of an equivalent inductor that would effectively replace the three inductors in each case. The equivalent inductance is defined so that dI/dt is the same when connected across that potential difference. In other words, find L_eq such that V = Assume that the three inductors are far enough apart that mutual inductance can be ignored.

Explanation / Answer

case 1) Inductors arranged in series

Leq= L1+L2+L3

case 2) Inductors conected in a parallel arranged

Leq= 1/L1 + 1/L2 + 1/L3 = ((L2+L3)+(L1L3)+(L1L2))/(L1L2L3)

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