Question

The solenoids S₁ and S₂ are wound on an iron-core of relative permeability 900. The area of their cross-section and their length are the same and are 4 cm² and 0.04 m, respectively. If the number of turns in S₁ is 200 and that in S₂ is 800, calculate the mutual inductance between the coils. The current in solenoid 1 is increased from 2A to 8A in 0.04 second. Calculate the induced emf in solenoid 2.

Answer 1

Given data:

μ_r = 900

A₂ = 4 × 10^-4 m²

l = 0.04 m

n₁ = 5000

n₂ = 20,000

i₁ =2A to i₂ = 8A

dt = 0.048

M = ?

ε₂ = ?

M = μ₀ μ_r n₁ n₂ A₂ l

M = 4π × 10^-7 × 900 × 5000 × 20000 × 4 × 10^-4 ×0.04

M = 4π × 90 × 4 × 4 × 10^-4

M = 18086 × 10^-4H

M = 1.81 H

induced emf,

ε₂ = M `"di"/"dt"`

ε₂ = `1.81 ((8 - 2)/0.04)`

ε₂ = `(1.81 xx 6)/(4 xx 106-2)`

= 2.715 × 10_-2 V

ε₂ = 271.5 V