PYQ Bank

Show that any arbitrary rotation axis is not permitted in a crystal lattice.

Explain the term critical magnetic field in a superconductor. How does the critical magnetic field vary with temperature in Type-I and Type-II superconductors ? What is Meissner effect ?

With a suitable circuit diagram and theory explain the use of OP-Amps as

(i) Adder, and

(ii) Integrator.

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Distinguish between a superconductor and perfect conductor. Explain what is a Cooper pair.

Lead in the superconducting state has critical temperature of 6.2\ \mathrm{K} at zero magnetic field and a critical field of 0.064\ \mathrm{MA\,m^{-1}} at 0\ \mathrm{K}. Determine the critical field at 4\ \mathrm{K}.

Show that the NAND gate is a universal gate.

For the logical equation given below, form the truth table and draw the corresponding logic circuit using different gates : Y = A \cdot B + \overline{A \cdot B}

The velocity of sound in f.c.c. gold and f.c.c. copper is 2100\,\mathrm{m/s} and 3800\,\mathrm{m/s} respectively. If the Debye temperature of copper is 348\,\mathrm{K}, then determine the Debye temperature of gold. Take the densities of gold and copper as 1.93 \times 10^{4}\,\mathrm{kg/m^3} and 0.89 \times 10^{4}\,\mathrm{kg/m^3} respectively.

X-ray of wavelength 1\cdot 4\text{ \AA} is found to be Bragg reflected from (111) plane of an fcc structure. If the lattice parameter of the crystal is 5\text{ \AA}, find the angle at which the X-ray beam is incident on the (111) plane of the crystal.

What is the reciprocal lattice and why is it named so? Derive the relationships for the primitive translation vectors of the reciprocal lattice in terms of those of the direct lattice.

Explain the working of SEM and TEM and highlight the major differences in principles. Draw neat schematic diagrams.

In a cubic unit cell, find the angle between normals to the plane (111) and (121).

An electric field of 100\ \mathrm{V/m} is applied to a sample of n-type semiconductor whose Hall coefficient is -0.0125\ \mathrm{m^3/coulomb}. Determine the current density in the sample assuming \mu_x = 0.36\ \mathrm{m^2\,V^{-1}\,s^{-1}}.

A silicon diode operates at a forward bias voltage of 0\cdot 4\text{ V}. Calculate the factor by which the current will be multiplied when the temperature is increased from 25^\circ\text{C} to 150^\circ\text{C} (\eta for \text{Si} = 2).

Explain with the help of a neat diagram the structure of a n-channel FET and its IV characteristics. In what way is an FET different from a BJT ?

How does the energy gap in superconductors differ from the energy gap in insulator? How does it vary with temperature for superconductors?

What is ac Josephson effect ? Derive an expression for the current flowing through the junction formed by two superconducting films separated by an insulator.

\questiondiagram{
} Explain how the circuit shown above can be a source of oscillations. Use this circuit to construct a transistor oscillator and explain its working. What is the frequency of oscillations of this circuit?

In an operational amplifier, the amplifier gain is 10000. The input series resistance is 100\text{ k}\Omega and the feedback resistance is 500\text{ k}\Omega. If the input voltage is 1\text{ volt}, find the exact output voltage and percentage error considering an infinite gain for the amplifier.