SPPU Electronics and Telecom Engineering (Semester 5)
Electromagnetics and Transmission Lines
December 2015
Total marks: --
Total time: --
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any one question from Q1 and Q2
1 (a) Derive the expression for electric field intensity E at a point 'P' due to infinite sheet charge with charge density 'ρs'.
6 M
1 (b) Derive the expression for the capacitance of spherical plate capacitor.
6 M
1 (c) A current sheet ( \overline K = 9\widehat a y ) A/M is located 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: ( \overline H_2 = 14.5\overline a_x + 8 \widehat a z ) A/M.
Find H1
8 M

2 (a) Derive the expression for the capacitance of parallel plate capacitor.
6 M
2 (b) Derive expression for Biot & savart law using magnetic vector potential.
6 M
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. Centened at origin & edges parallel to the axis.
8 M

Solve any one question from Q3 and Q4
3 (a) Select values of K such that each of the following pairs of fields satisfies Maxwells's equation [ i) \ \overline E = (K_x - 100t)overline ab_y \ v/m \ \ \ \overline H= (x+20t) \overline a_z \ A/m \ \ \mu = 0.25 \ H/m \ \epsilon =0.01 \ F/m. \ ii) \ \overline D = 5x\overline a \ x-2y \ \overline a \ y+kz \ \overline a z \ \mu c /m^2 \ \ \overline {B} = 2 \overline a_y \ mT \ \ \mu = \mu_0 \ \epsilon = \epsilon_0 ]
8 M
3 (b) Define displacement current and displacement current density & hence show that ∇×H=Jc+Jd
where JC → conduction current density
Jd → displacement current density.
8 M

4 (a) Derive Maxwell's equations in differential and integral form for time varying and free space.
8 M
4 (b) What is mean by uniform plane wave? obtain the wave equation travelling in free space in terms of E.
8 M

Solve any one question from Q5 and Q6
5 (a) Explain the phenomenon of reflection of transmission line and hence define reflection coefficient.
6 M
5 (b) A transmission line cable has the following primary constants.
G=0.8 μmho/km
L=0.00367 H/km
C=8.35 nF/km.
At a signal of 1 KHz calculate
i) Characteristic impedance Zo
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 M

6 (a) A cable has an attenuation of 3.5 dB/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 10km down the line when line is terminated with Zo.
8 M
6 (b) Derive the expression for characteristic impedance (Zo) and propagation constant (r) in terms of primary constants of transmission line.
8 M

Solve any one question from Q7 and Q8
7 (a) Derive the expression for input impedance of a transmission line. Hence state the effect of open circuit & short circuit of line or input impedance.
9 M
7 (b) Explain standing wave and why they generate? Derive the relation between the SWR and magnitude of reflection coefficient.
9 M

8 (a) What is impedance matching? Explain necessity of it, What is stub matching? Explain the single stub matching with its merits & demerits.
8 M
8 (b) The VSWR on a lossless line is found to be '5' and successive voltage minima are 40 cm apart. The first voltage minima is observed to be 15cm from load. The length of a line is 160 cm and characteristic impedance is 300 Ω. Using smith chart find load impedance sending end impedance.
10 M

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