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? (Answer: 30 Wb)



Given:

Mutual Inductance = M = 1.5 H

Initial current  = I₁ = 0 A

Final current  = I₂ = 20 A

So change in current △I = I₂ - I₁ = 20 A - 0 A = 20 A

Change in time interval = △t = 0.5 s



To Find:

Change in the magnetic flux = Δф = ?


Solution:

We can't find `\Δф_B` directly from the given data, so we can deduce a relation, therefore, using the relation of  Faraday's Law

Ɛ = `\frac {Δф_B}{Δt}` -------------(1)

and formula for induced e.m.f in mutual inductance

Ɛ = M `\frac {ΔI}{Δt}` --------------(2)

by comparing the equation (1) and (2) we get

`\frac {Δф_B}{Δt}` = M `\frac {ΔI}{Δt}` 

or 

 `\Δф_B` = M ΔI

by putting values

 `\Δф_B` = 1.5 H  ｘ 20 A

 `\Δф_B` = 30 Wb ------------Ans.

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⭐ Weber 'Wb' is the unit of measurement for Magnetic Flux:

1 Wb =  H A = V s = kg m² s⁻² A⁻¹



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