Answer / Explanation
To start with in answering this question, let us first recall the equation used in calculating the percentage of reflected power:
That is:
Reflected Power = %Pref = 100 ║Γ║²........let this be equation (1)
Taking note from the expression above that:
Γ = Reflection Coefficient.
The reflection coefficient is the variable that shows the level of electromagnetic wave that is reflected by an impedance break in the transmission medium.
Now, recalling the expression in finding the reflection coefficient,
we have: Γ = η₂ - η₁ / η₂ +η₁ ...............let this be equation (2)
Where:
η₁ and η₂ = intrinsic Impedance
Now, if we recall the relationship between intrinsic impedance and relative permitivities,
We have: η₂ / η₁ = √ εr₁ / εr₂
Now, if we refer back to the narrative of the question, we will substitute 1.78 for εr₂ and substitute 1 for εr₁
So, moving forward, we have:
η₂ / η₁ = √ 1 / 1.78
η₂ / η₁ = 0.7495
η₂ = 0.7495 η₁ ..............let this be equation (3)
Now, moving forward, we will substitute equation (3) into equation (2)
Therefore, we have:
Γ = 0.7495 η₁ - η₁ / 0.7495 η₁ + η₁
Γ = - 0.2505η₁ / 1.7495η₁
Γ = - 0.1431
Now, we go ahead to substitute the value of the reflection coefficient into equation (1)
Thus, we have:
Recalling equation (1):
%Pref = 100 ║Γ║²
%Pref = 100 x ( 0.1431) ²
= 2.0477%
Approximating the value above, we will have:
%Pref = 2.05%
Therefore, we can conclude that the percentage of power that is reflected is 2.05%