Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II ELECTROMAGNETIC THEORY AND TRANSMISSION LINES Previous Question Paper (September/October - 2023 - R13)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
Four equal point charges Q = 20nC are located at 1, 2, 3 and 4 m. Find the potential at origin.
Answer
The electric potential V at the origin due to a point charge Q at a distance r is given by the formula:
Given four equal charges Q = 20 × 10-9 C located at distances r = 1, 2, 3, and 4 m from the origin, the total potential is the sum of the individual potentials:
Using 1 / (4πε₀) ≈ 9 × 109 N·m²/C²:
A circular disc of radius 5m with a surface charge density ρs = 10sinφ is enclosed by surface. What is the net flux crossing the surface?
Answer
According to Gauss's Law, the net electric flux Φ crossing a closed surface is equal to the total charge Q enclosed by that surface divided by the permittivity of free space ε₀. The total charge Q is found by integrating the surface charge density ρs over the area of the circular disc:
Given the disc of radius a = 5m lies in the xy-plane, the differential area element in polar coordinates is dA = r dr dφ. The integration limits are r from 0 to 5 and φ from 0 to 2π:
Evaluating the integral:
Since the total enclosed charge Q is 0, the net flux Φ = Q/ε₀ is 0.
Calculate the emf when the flux is given by 5sin t + 4cos t.
Answer
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Find the work done in an inductor of 12H when a current 0.3A is passed through it.
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In free space, the ratio of frequency to the velocity of light gives the phase constant. Comment on this.
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Find the refractive index of a material with permittivity 1.4.
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The attenuation constant causes phase distortion and the phase constant causes frequency distortion. Comment on this.
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The length of a transmission line is same as that of the wavelength of the signal and the load is 50 ohms. Determine the input impedance.
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A short circuited line is having 100 ohms characteristic impedance. Determine the input impedance.
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If the maxima and minima voltage of the standing wave are 4 and 1.6 respectively. Determine the standing wave ratio.
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Part B
Establish Gauss Law in point form and integral form. Give its usefulness with an illustrative example.
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The point Charges -1nc, 4nC, and 3nC are located at (0,0,0),(0,0,1) and (1,0,0), respectively. Find the energy in the System.
Answer
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Prove that E = -∇V.
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Point charges 1 mC and -2mC are located at (3,2,-1) and (-1,-1,4) respectively. Calculate the electric force on a 10nC charge located at (0,3,1) and the electric field intensity at that point.
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State and explain Ampere’s law and also mention its applications.
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Derive the electric field boundary conditions between dielectric and conductor for time varying fields.
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Explain the concept of displacement current density with necessary equations.
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An electron with velocity u = (3ax + 12 ay - 4az) 10^5 m/s experiences no net Force at a point in a magnetic field B = 10ax + 20ay + 30az mWb/m^2. Find E at that point.
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Derive reflection coefficient of E & H fields when Uniform plane wave propagating from dielectric to conductor Medium.
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A uniform wave in air has E = 10cos(2π × 10^6 t – βz)ay V/m. Calculate β and λ.
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Discuss poynting theorem. Write the significance of it.
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A signal in air (z≥0) with the electric field component E = 10sin(ωt+3z)ax V/m, hits normally the ocean surface is smooth and that ε = 80ε0, μ = μ0, σ = 4 S/m in ocean, determine i) ω ii) The wavelength of the signal in air.
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List out the various transmission lines. Write the applications of transmission lines.
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The constants per km of a certain cable are: R = 6.75 ohms; L = 5.5 mH; C = 0.00872 μf and G = 0.4 μ mhos. Calculate the Characteristic impedance, attenuation constant and phase velocity, when ω = 5000 radians per second.
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Differentiate between phase and group velocities with illustrative examples.
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A distortion less line has Z0 = 60Ω, α = 20 mNp/m, u = 0.6c, where c is the Speed of light in vacuum. Find R, L, G, C and λ at 100MHz.
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Give the steps involved in single stub matching.
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The observed standing wave ratio on a 100Ω lossless line is 8. If the first maximum voltage occurs at 0.3λ from the load, calculate the load impedance.
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List out the advantages and applications of smith chart.
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A short –circuited Coaxial transmission line has Z0 = 60Ω and γ = j8.5/m. Calculate the input impedance, if the length of the line is i) 25 cm ii) 2.5m.
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