A pair of adjacent coils has a mutual inductance of 0.75 H. If the current in the primary changes from 0 to 10 A in 0.25 s, what is the average induced emf in the secondary? What is the change in flux in it if the secondary has 500 turns? (Answer: 300 V, 1.5 𝐱 10⁻¹ Wb). 



Data Given:

Mutual Induction = M = 0.75 H

Current change in primary coil = `\△I_p` = 10 A - 0 A = 10 A

Time interval = △t = 0.25 s

Number of turns in secondary coil = Nₛ = 500 turns


To Find:


Induced emf in secondary coil = `\Ɛ_S` = ?

Change in flux = Δф = ?


Solution:

Using the following relation

`\Ɛ_S` =  M `\frac {△I_p}{Δt}`  --------(1)


by putting the corresponding values

`\Ɛ_S` =  0.75 H ｘ`\frac {10 A}{0.25 s}`

`\Ɛ_S` =  30 V  ---------------Ans.1


We have another relation for induced emf in the secondary coil.

`\Ɛ_S` = Nₛ `\frac {Δф}{Δt}` -------------(2)

by comparing equations (1) and (2)

Nₛ `\frac {Δф}{Δt}` = M `\frac {△I_p}{Δt}`

or

Δф = `\frac {M}{Nₛ}` ｘ ΔI_p 

by putting values

Δф = `\frac {0.75 H}{500}` ｘ 10 A

Δф = 0.15 Web

or

Δф = 1.5 ｘ 10⁻¹ Web ------------Ans.2




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