When two or more inductors are connected in such a way that same current flows through them, then it is said that they are connected in series. Like series connection of resistors , series connected inductors can be replaced by an equivalent inductor. Let us assume that ‘n’ inductors having inductance of L 1 , L 2 , L 3 ,…L n Henry are connected in series as shown in figure below. Since same current I is flowing through each of the inductors therefore voltage drop across inductors L 1 , L 2 , L 3 , …..L n will be L 1 di/dt, L 2 di/dt, L 3 di/dt, …..L n di/dt respectively. Therefore from Kirchhof’s voltage law, V = L 1 di/dt + L 2 di/dt + L 3 di/dt + ……..+ L n di/dt = di/dt (L 1 + L 2 + L 3 +…….+L n ) …………….(1) If the series connected inductors are replace by a single equivalent inductor Le then V = L e di/dt …………………….(2) Comparing equation (1) and (2) we get, L e = L 1 + L 2 ...
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