PYQ Bank

Show that the London equation \vec{\nabla} \times \vec{J} = -\frac{1}{\mu_0\lambda_L^2}\vec{B} or \vec{j} = -\frac{c}{4\pi n\lambda_L^2}\vec{A} leads to the Meissner effect.

Write down London second equation for superconductors. Explain how it accounts for the Meissner effect.

A perfect conductor and a superconductor with T_c \sim 10\ \mathrm{K} are subjected to the following conditions:

(i) cooled under applied magnetic field to 4\ \mathrm{K}

(ii) cooled to 4\ \mathrm{K} and then magnetic field is applied with schematic diagrams, explain path of magnetic field lines in all these situations.

Starting with the expression for the density of states for electrons in a band, show that the Fermi energy of an intrinsic semiconductor is at the middle of the band gap. Use these results to estimate the electron density at 300 K (Assuming E_g=1\,\mathrm{eV} and the rest masses of electron and hole as m_e and m_h).

Draw and explain the collector characteristics of a bipolar junction transistor in common emitter configuration. Using the plot, explain how the transistor can be used as an ON-OFF switch.

Can you comment from the above question whether you can use it to scan surface by microscopy?

Prove the following Boolean identity and draw its gates equivalent : Y = \bar{B}(A + C) + C(\bar{A} + B) + AC

Construct a digital circuit to add three bits A, B and C and provide their sum and carry as outputs. Show appropriate Boolean expressions and truth table to justify the outputs.

What is a thermistor? Discuss static characteristics of a thermistor. What is its time constant?

\questiondiagram{
} A crystal plane is shown in the above figure. Find its Miller indices and interplanar spacing.

A type I superconductor with T_c = 7\text{ K} has slope \frac{dB_c}{dT} = -25\text{ mT/K} at transition temperature T_c. Estimate its critical field at 6\text{ K}.

Explain the variation of Magnetisation of Type I and Type II superconductors as a function of applied magnetic field.

Metallic iron undergoes a structural phase transition from bcc to fcc at 910^\circ\mathrm{C}. At this temperature, the atomic radii of iron atoms in the bcc and fcc structures are 0.126 \times 10^{-9}\,\mathrm{m} and 0.129 \times 10^{-9}\,\mathrm{m} respectively. Calculate the volume change in percentage during this structural change.

Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility \psi. Plot and explain the variation of \frac{1}{\psi} with temperature for the three materials.

For a simple cubic, a face centered cubic and a body centered cubic crystal, determine the atomic packing factor. How many atoms per \text{mm}^2 surface area are there in (100) plane for leads which has f.c.c. structure. The radius of the atoms is 0\cdot 174\text{ nm}.

What are the rules followed in biasing a bipolar junction transistor when it is used as an amplifier? Show how n-p-n and p-n-p transistors to be used as an amplifier are biased and the direction of flow of base, collector and emitter currents.

Construct an operational amplifier based analog computer to solve the differential equation \frac{d^2v}{dt^2}-\frac{dv}{dt}+2v=0.

A power supply using a full-wave rectifier is to provide 100\text{ mA} at 20\text{ V} with no more than 1\% ripple. Calculate the minimum value of smoothing capacitor used. Consider the diode resistance and the resistance of the secondary of the transformer as negligible. Also take ripple frequency as 50\text{ cycles per second}.

(i) What is De Morgan's law ? (ii) Simplify the Boolean expression A + AB + ABC + ABCD

Explain the race problem encountered in an RS latch and how it can be avoided. Build a Mod-10 counter using JK flip-flops and explain its working.