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Numerical

A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

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#### Solution

Mutual inductance of a pair of coils, µ = 1.5 H

Initial current, I_{1} = 0 A

Final current I_{2} = 20 A

Change in current, dI = I_{2} − I_{1} = 20 − 0 = 20 A

Time taken for the change, t = 0.5 s

Induced emf, `"e" = ("d"phi)/"dt"` ............(1)

Where `"d"phi` is the change in the flux linkage with the coil.

Emf is related with mutual inductance as:

`"e" = mu "dI"/"dt"` .......................(2)

Equating equations (1) and (2), we get

`("d"phi)/("dt") = mu("dl")/"dt"`

`"d"phi` = 1.5 × (20)

= 30 Wb

Hence, the change in the flux linkage is 30 Wb.

Concept: Inductance - Mutual Inductance

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