Solve your IGNOU Doubts

Question:

a) For a conductor, number of collisions per second is $10^{12},$ and plasma frequency is $\omega _P=2\pi \times 10^{15}.$

Calculate the skin depth for the signal frequency of (i) 50 $Hz,$ and (ii) 50 MHz.

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Question:

Obtain the Laplace transform of the function: $f(t)=(t^{2}+4t+5)e^{4t}$

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Question:

b) Explain the use of step input signal in characterizing a communication system. Why square wave signal is preferred over step input signal?

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Question:

a) What are the characteristics of the first stage amplifier of an audio receiver circuit?

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Question:

Obtain the Fourier transform of the following functions:

i) $f(x)\left\{\begin{matrix} 0,& for &-\infty <x<-a/2 \\ 1, &for & -a/2<x<a/2 \\ 0. & for & a/2<x<\infty \end{matrix}\right.$

ii) $f(x)\left\{\begin{matrix} e^{-x/a}, & x>0 \\ 0, & otherwise \end{matrix}\right.$

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Question:

i) The best mode for transmitting optical signal is Line-of-Sight communication.

ii) A simple sine wave signal does not carry any information.

iii) Input impedance for an open ended transmission line of $\lambda /2$ length is zero.

iv) Amplitude distortion in AM gives rise to unwanted frequency components.

v) Amplitude shift keying is modulation of digital carrier by analog signal.

vi) Mobile telephony uses time division multiplexing.

vii) Gunn devices can be built using indirect band gap semiconductors.

viii) In television, vertical scanning frequency is higher than horizontal scanning frequency.

ix) Machine language programmes are portable, while assembly language programmes are not.

x) Router can provide inter-conversion of protocols among connections.

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Question:

d) If the temperature of the background radiation today is $3\,K,$ at what time after the birth of the universe was the temperature $10^{15}K.$ Take the age of the universe as $15\times 10^9$ years.

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Question:

c) What is cosmic background radiation? Explain why it is so important to the debate between evolving and a steady-state universe.

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Question:

b) With the help of a diagram, explain the unified scheme for understanding active galactic nuclei.

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Question:

a) Describe Hubble’s Classification scheme for galaxies.

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Question:

d) Describe the composition of the interstellar medium. Explain how it has been possible to map the HI clouds.

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Question:

c) The mean free path of photons in stars is of the order of 0.2 cm. Show that the time taken for a photon to reach the surface of a star of radius 4 $R_e$ is of the order of one million year.

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Question:

Obtain the Taylor series expansion of $f(z)={\frac{1}{z^{2}+4}}\ \ {\mathrm{about}}\ z=-i.$

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Question:

b) Derive the expression for the mean temperature in a star:

$<T>\propto M^{2/3}<\rho >^{1/3}$

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Question:

Prove that $u=x^2-y^2$ and $v=\frac{y}{x^2+y^2}$ are harmonic functions of (x, y).

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Question:

a) Derive Jeans criteria for the stability of a gas cloud. A collapsing cloud is made only of neutral hydrogen (H1). If the temperature of the cloud is 50 K and its number

density is $10^5\,m^{-3},$ calculate its Jeans mass.

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Question:

Evaluate the integral

$\textstyle\int_{0}^{2\pi}{\frac{\sin^{2}(\theta\,\mathrm{d}\theta\,\mathrm{d}\theta\,}{5-4\,\cos\mathrm{d}}}\,$

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Question:

c) Derive an expression for the tidal force for the earth-moon system and show that its magnitude depends on the latitude. Explain tidal bulge on the basis of this expression.

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Question:

b) Explain how sunspots survive for so long even though they are surrounded by hotter matter

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Question:

a) Explain how we estimate the effective surface temperature of the Sun. A main sequence star has mass $2\times 10^{31}$ kg and radius $3\times 10^{9}$ m.Obtain an estimate of the average temperature throughout the star.