A circuit has 1000 turns enclosing a magnetic circuit 20 cm² in section with 4 A current, the flux density is 1 Wb m⁻² and with 9A current, it is 1.4 Wb m⁻². Find the mean value of the inductance between these current limits and the induced e.m.f. if the current falls from 9A to 4A in 0.05s. (Answer: 0.16H, 16V)



Data Given:

Numbers of turns = N = 1000 turns

Area of the circuit = A = 20 cm² = 0.0020 m²

Initial current = I₁ = 4 A

Initial magnetic flux density = B₁ = 1 Wb m⁻²

Final current = I₂ = 9 A

Final magnetic flux density = B₂ = 1.4 Wb m⁻²

Change in time interval = △t = 0.05 s

To Find:

Self-inductance = L = ?

Induced e.m.f. = Ɛ = ?

Solution:

The formula for self-induction is given by:

L = `\frac {N Δф}{ΔI}` 

 where Δф = Magnetic Flux = ΔB • A 

L = `\frac {N ΔB • A}{ΔI}` 

or

L = NA `\frac {ΔB }{ΔI}`  --------------(1)

Where 

ΔB = B₂ - B₁ = 1.4 Wb m⁻² - 1 Wb m⁻² = 0.4 Wb m⁻²

ΔI = I₂ - I₁ = 9 A - 4 A =  5 A 


Now putting all the corresponding values in equation (1)


L = 1000 ｘ 0.0020 m² ｘ`\frac {0.4 Wb m⁻²}{5 A}`

L = 2 ｘ 0.08 Web A⁻¹

or

L = 0.16 H ------------------ Ans.


------------------------------------

To find the Induced e.m.f. by Using another formula for self-inductance 

L = Ɛ `\frac {Δt}{ΔI}`

or 

Ɛ =  L `\frac {ΔI}{Δt}`

by putting the corresponding values

Ɛ =  0.16 H ｘ `\frac {5 A}{0.05 s}`

Ɛ =  16 V -------------------Ans.(2)



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