Question

A plane traveling wave has a peak electric field E₀ of 15 V/m. The medium is lossless with μ_r = 1 and ϵ_r = 12, find the impedance of the medium:
1. η = 108.83 Ω
2. η = 106.25 Ω
3. η = 108.83 × 10^-2 Ω
4. None of these

Answer 1

Correct Answer - Option 1 : η = 108.83 Ω

Explanation:

Intrinsic Impedance of plane traveling wave:

1. Intrinsic impedance of a medium can be defined as the impedance which an electromagnetic wave faces while traveling in a medium.

2. It is also defined as the ratio of the electric field to the magnetic field.

3. The intrinsic impedance of a medium is given by:

\(η =\sqrt{\frac{j\omega \mu }{σ\ +\ j\omega \epsilon }}~\)    ---(1)

Where μ = Magnetic permeability of the medium.

And ϵ = Electric permittivity of the Medium.

For lossless or perfectly dielectric medium,

σ = 0 

Putting σ = 0 in equation (1) we get

\(η =\sqrt{\frac{j\omega \mu }{j\omega \epsilon }}=~\sqrt{\frac{\mu }{\epsilon }}\)      ---(2)

Given, μ_r = 1, ϵ_r = 12

ϵ_o = ϵo ϵ_r, μ = μ_o μ_r

μ_o = 1.2566 × 10^-6 H / m

ϵo = 8.85 × 10^-12 F / m

From equation (2),

 \(η =~\sqrt{\frac{\mu }{\epsilon }}=\sqrt{\frac{1.2566\ ×\ 10^{-6}}{12\ ×\ 8.85\ ×\ 10^{-12}}}=108.83\ Ω\)

So, impedance = 108.83 Ω

 

For free-space, the intrinsic impedance is a real quantity, i.e.

\(\eta_0=\sqrt \frac{\mu_0}{\epsilon_0} \ = \ 120\pi\)