First slide

Inductance

Question

Two identical induction coils each of inductance L joined in series are placed very close to each other such that the winding direction of one is exactly opposite to that of the other. What is the net inductance?

Moderate

A

L²
B

2L
C

L/2
D

Zero

Solution

Since the windings of the coils are opposite , equivalent inductance of the coils is given by
$L_{e} = L_{1} + L_{2} - 2 M . S i n c e t h e c o i l s a r e p l a c e d v e r y c l o s e t o e a c h o t h e r M = \sqrt{L_{1} L_{2} .} T h e r e f o r e L_{e} = {(\sqrt{L_{1}} - \sqrt{L_{2}})}^{2} = {(\sqrt{L} - \sqrt{L})}^{2} = 0$

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