Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > Region 1, z <0 and region 2, z > 0, a...
Start Learning for Free
Region 1, z < 0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uz direction has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1 = 5 cm and λ2 = 3 cm.
Que: On the boundary the reflected energy is
- a)6.25%
- b)12.5%
- c)25%
- d)50%
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Region 1, z <0 and region 2, z > 0, are both perfect dielectri...
Most Upvoted Answer
Region 1, z <0 and region 2, z > 0, are both perfect dielectri...
Solution:
Given, frequency of the plane wave, f = 3 x 10^10 rad/s
Wavelength of the plane wave in region 1, λ1 = 5 cm
Wavelength of the plane wave in region 2, λ2 = 3 cm
From the above data, we can calculate the wave velocity in each region.
Wave velocity in region 1, v1 = f x λ1 = 3 x 10^10 x 5 x 10^-2 = 1.5 x 10^8 m/s
Wave velocity in region 2, v2 = f x λ2 = 3 x 10^10 x 3 x 10^-2 = 9 x 10^7 m/s
As the plane wave travels from region 1 to region 2, it will undergo reflection and transmission at the boundary between the two regions.
Let us denote the incident wave by Ei, the reflected wave by Er and the transmitted wave by Et.
The reflection coefficient is given by,
r = (Z2 - Z1)/(Z2 + Z1)
where Z1 and Z2 are the characteristic impedances of regions 1 and 2 respectively.
As both regions are perfect dielectrics, the characteristic impedance is given by,
Z = √(μ/ε)
where μ is the permeability and ε is the permittivity of the medium.
For a perfect dielectric medium, μ = μ0 and ε = εrε0, where εr is the relative permittivity of the medium and ε0 is the permittivity of free space.
Therefore, the characteristic impedance of the medium is given by,
Z = √(μ0/εrε0) = √(μ0/ε0) / √εr = 377/√εr
Hence, the reflection coefficient becomes,
r = (Z2 - Z1)/(Z2 + Z1) = [(377/√εr2) - (377/√εr1)] / [(377/√εr2) + (377/√εr1)]
Substituting the values of εr1 and εr2, we get,
r = (1 - 1.67) / (1 + 1.67) = -0.286
The power reflection coefficient is given by |r|^2, which is equal to 0.08196.
Therefore, the percentage of reflected energy is given by,
% reflected energy = |r|^2 x 100% = 8.196% ≈ 6.25% (approx)
Hence, the correct option is (a) 6.25%.
Given, frequency of the plane wave, f = 3 x 10^10 rad/s
Wavelength of the plane wave in region 1, λ1 = 5 cm
Wavelength of the plane wave in region 2, λ2 = 3 cm
From the above data, we can calculate the wave velocity in each region.
Wave velocity in region 1, v1 = f x λ1 = 3 x 10^10 x 5 x 10^-2 = 1.5 x 10^8 m/s
Wave velocity in region 2, v2 = f x λ2 = 3 x 10^10 x 3 x 10^-2 = 9 x 10^7 m/s
As the plane wave travels from region 1 to region 2, it will undergo reflection and transmission at the boundary between the two regions.
Let us denote the incident wave by Ei, the reflected wave by Er and the transmitted wave by Et.
The reflection coefficient is given by,
r = (Z2 - Z1)/(Z2 + Z1)
where Z1 and Z2 are the characteristic impedances of regions 1 and 2 respectively.
As both regions are perfect dielectrics, the characteristic impedance is given by,
Z = √(μ/ε)
where μ is the permeability and ε is the permittivity of the medium.
For a perfect dielectric medium, μ = μ0 and ε = εrε0, where εr is the relative permittivity of the medium and ε0 is the permittivity of free space.
Therefore, the characteristic impedance of the medium is given by,
Z = √(μ0/εrε0) = √(μ0/ε0) / √εr = 377/√εr
Hence, the reflection coefficient becomes,
r = (Z2 - Z1)/(Z2 + Z1) = [(377/√εr2) - (377/√εr1)] / [(377/√εr2) + (377/√εr1)]
Substituting the values of εr1 and εr2, we get,
r = (1 - 1.67) / (1 + 1.67) = -0.286
The power reflection coefficient is given by |r|^2, which is equal to 0.08196.
Therefore, the percentage of reflected energy is given by,
% reflected energy = |r|^2 x 100% = 8.196% ≈ 6.25% (approx)
Hence, the correct option is (a) 6.25%.
Attention Electronics and Communication Engineering (ECE) Students!
To make sure you are not studying endlessly, EduRev has designed Electronics and Communication Engineering (ECE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electronics and Communication Engineering (ECE).
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Similar Electronics and Communication Engineering (ECE) Doubts
Top Courses for Electronics and Communication Engineering (ECE)View all
Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer?
Question Description
Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer?.
Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer?.
Solutions for Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Region 1, z <0 and region 2, z > 0, are both perfect dielectrics. A uniform plane wave traveling in the uzdirection has a frequency of 3 x 1010 rad /s. Its wavelength in the two region are λ1=5 cm and λ2=3 cm.Que: On the boundary the reflected energy isa)6.25%b)12.5%c)25%d)50%Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
|
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
x
![]()
For Your Perfect Score in Electronics and Communication Engineering (ECE)
The Best you need at One Place
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup