Question Paper: Electromagnetics and Transmission Lines : Question Paper Jun 2015 - Electronics & Telecom Engineering (Semester 5) | Pune University (PU)
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## Electromagnetics and Transmission Lines - Jun 2015

### Electronics & Telecom Engineering (Semester 5)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.

### Answer any one question from Q1 and Q2

1 (a) Derive the expression for electric field intensity E at a point 'P' due to infinite line charge with uniform line charge density 'ΡL'.(6 marks) 1 (b) Derive Laplace and Poisson equations for electronics & hence state physical significance of Laplace & Poisson equations.(6 marks) 1 (c) A current sheet k = 9ay A/m is locate at z=0. The region 1 which is at z<0 has μr1=4 and region 2 which is at z>0 has μr2=3.
Given H2 =14.5ax + 8az A/m Find H1.
(8 marks)
2 (a) Derive the expression for the capacitance of spherical plate capacitor.(6 marks) 2 (b) Derive expression for Biot & Savart law using magnetic vector potential.(6 marks) 2 (c) $$\overline D = \dfrac {5x^3} {2} \widehat a x \ c/m^2 .$$ Prove divergence theorem for a volume of cube of side 1m. Centered at origin & edges parallel to the axis.(8 marks)

### Answer any one question from Q3 and Q4

3 (a) Define displacement current and displacement current density & hence show that \nabla \times H = J_c + J_d \\ \begin {align*} where & J_c \rightarrow \ conduction \ current \ density \\ &J_d \rightarrow \ Displacement \ current \ density \end{align*}(8 marks) 3 (b) Select values of K such that each of the following pairs of fields satisfies Maxwell's equation. $$i) \ \overline E = (Kx - 100t) \overline a_y \ V /m \\ \ \ \overline H = (x+20t)\overline a_z \ A/m \\ \ \ \mu=0.25 H/m \ \varepsilon=0.01F /m \\ \\ ii) \overline D = 5x \widehat a_x - 2 y \widehat a_y + Kz \widehat a _z \ \mu c/ m^2 \\ \ \ \overline B = 2 \overline a_y \ mT \\ \ \ \mu = \mu_0 \ \varepsilon= \varepsilon_0$$(8 marks) 4 (a) What is mean by uniform plane wave, obtain the wave equation travelling in free space in terms of E.(8 marks) 4 (b) Derive Maxwell's equations in differential and integral form for time varying and free space.(8 marks)

### Answer any one question from Q5 and Q6

5 (a) Derive the expression for characteristic impedance (Z0 ) and propagation constant (r) in terms of primary constants of transmission line.(8 marks) 5 (b) A cable has an attenuation of 3.5dB/Km and a phase constant of 0.28 rad/km. If 3V is applied to the sending end then what will be the voltage at point 10 km down the line when line is terminated with Z0.(8 marks) 6 (a) Explain the phenomenon of reflection of transmission line and hence define reflection coefficient.(6 marks) 6 (b) A transmission line cable has following primary constants.
R=11 Ω / km, G=0.8 μ℧ / km
L=0.00367 H/Km C=8.35 nF/km
At a signal of 1 kHz calculate

i) Characteristic impedance Z0
ii) Attenuation constant (α) in Np/Km
iii) Phase constant (β) in radians / Km
iv) Wavelength (λ) in Km
v) Velocity of signal in Km/sec.
(10 marks)

### Answer any one question from Q7 and Q8

7 (a) What is the impedance matching? Explain necessity of it, what is stub matching? Explain the single stub matching with its merits and demerits.(9 marks) 7 (b) Explain standing wave and why they generate? Derive the relation between the SWR and magnitude of reflection coefficient?(9 marks) 8 (a) What do you mean by distortionless line. Derive expression for characteristic impedance and propagation constant for distortionless line.(8 marks) 8 (b) The VSWR on a lossless line is found to be '5' and successive voltage minima are 40 cm a part. The first voltage minima is observed to be 15 cm from load. The length of a line is 160cm and characteristic impedance is 300 Ω Using Smith chart find load impedance, sending end impedance.(10 marks)