Question

Two media are characterized as:
1. ε_r = 1, μ_r = 4 and σ = 0 
2. ε_r = 4, μ_r = 4 and σ = 0
Where

ε_r = relative permittivity
μ_r = relative permeability
σ = conductivity
The ratio of the intrinsic impedance of the media 2 to media 1 is

1. 2 : 1
2. 1 : 2
3. 1 : 1
4. 2 : 2

Answer 1

Correct Answer - Option 2 : 1 : 2

Concept:

Intrinsic Impedance(η):

It is given by \({\rm{\eta }} = \sqrt {\frac{{{\rm{j\omega \mu }}}}{{{\rm{σ }} + {\rm{j\omega \epsilon}}}}} \)

if σ = 0 then

\(η = \sqrt {\frac{μ }{{ϵ}}} \)

where μ = μ₀μ_r  and ϵ = ϵ₀ϵ_r

ϵ_r = relative permittivity
μ_r = relative permeability

Calculation:

given that 

media 1 → ε_r = 1, μ_r = 4 and σ = 0 
media 2 → ε_r = 4, μ_r = 4 and σ = 0

η₁ : η₂ = \(\sqrt {\frac{μ_1 }{{ϵ_1}}}\): \(\sqrt {\frac{μ_2 }{{ϵ_2}}}\)

η1 : η₂ = \(\sqrt {\frac{4}{{1}}}\): \(\sqrt {\frac{4 }{{4}}}\)

η₂ : η₁ = 1 : 2