# GATE Papers >> EEE >> 2015 >> Question No 156

Question No. 156

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $\alpha$L is obtained by interconnecting these two coils, the minimum value of $\alpha$ is ________.

Solution of Question No 156 of GATE 2015 EEE Paper

Case-I

${\mathrm L}_{\mathrm{eff}.}={\mathrm L}_1+{\mathrm L}_2=2\mathrm L,\mathrm a=2$

case-II

${\mathrm L}_{\mathrm{eff}.}=\frac{{\mathrm L}_1{\mathrm L}_2}{{\mathrm L}_1+{\mathrm L}_2}=\frac{\mathrm L^2}{2\mathrm L}=\frac{\mathrm L}2,\;\mathrm a=0.5$

Case-III

If both are differentially coupled then

${\mathrm L}_{\mathrm{eff}.}=0$

Minimum value = 0

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