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(i) Distinguish between d.c. Josephson effect and a.c. Josephson effect. Show that Josephson effect exhibits the quantum interference phenomenon on macroscopic scale. (ii) The critical magnetic field of superconducting niobium is 1 \times 10^5\text{ A/m} at 8\text{ K} and 2 \times 10^5\text{ A/m} at 0\text{ K}. Calculate the critical transition temperature (T_c) of niobium.
What is Meissner effect? Show that the Maxwell's equation is in contradiction to the Meissner effect. What are the inferences from this contradiction?
Show that for an n-type semiconductor, the Fermi level lies midway between the donor states and the conduction band edge at low temperature (assuming E_v=0).
The wavelength of a prominent X-ray line from a copper target is 0.1512\,\mathrm{nm}. The radiation, when diffracted with (111) plane of a crystal with fcc structure, corresponded to a Bragg angle of 20.2^\circ. If the density of the crystal is 2698\,\mathrm{kg/m^3} and atomic weight is 26.98\,\mathrm{kg/kmol}, calculate the Avogadro number.
Considering atoms hard, uniform spheres, find the number of atoms per unit cell and packing fraction for simple cubic, bcc and fcc structures.
(i) Prove the following using De Morgan's theorems : A \cdot B + C \cdot D = \overline{\overline{A \cdot B} \cdot \overline{C \cdot D}} (ii) Simplify the following expression : Y = A \cdot B \cdot \bar{C} \cdot D + \bar{A} \cdot B \cdot \bar{C} \cdot \bar{D} + B \cdot \bar{C} \cdot D
Explain why Type-II superconductor is better than Type-I superconductor in the application of superconductor magnets.
Why NAND and NOR gates are called universal gates? Give the logic diagram, Boolean equation and the truth table of a X--OR gate.
Describe briefly the functions of the basic segments of a microprocessor. Draw a block diagram of the registers in the 8085 microprocessor.
Compare the dependence of resistance on temperature of a superconductor with that of a normal conductor. Describe briefly the formation of Cooper pairs.
An n-p-n transistor with \alpha = 0\cdot 98 is operated in the CB configuration. If the emitter current is 3\text{ mA} and the reverse saturation current is I_{CO} = 10\text{ }\mu\text{A}, what are the base current and the collector current?
(i) Diamond and silicon have similar band structure. Why is diamond an insulator while silicon a semiconductor? (ii) An insulator has an optical absorption which occurs for all wavelengths lesser than 1400\text{ \AA}. Find the width of the forbidden energy band for the insulator.
Why is the Field Effect Transistor (FET) called Unipolar Transistor? Discuss how it is superior than Bipolar Junction Transistor.
Explain the drawbacks of Einstein's theory of specific heat and how it was overcome by Debye.
State the basic conditions for oscillations in a feedback amplifier. What are the primary requirements to obtain steady oscillations at a fixed frequency?
Explain the high temperature superconductivity. What are different properties of high temperature superconductors ?
Draw the circuit diagram of a transistor operating in the common-base configuration and sketch its input and output characteristics. Indicate the active, cut-off and saturation regions.
An X-ray beam of wavelength \lambda_1 undergoes a first order Bragg reflection at a Bragg angle of 30^\circ. X-ray of wavelength 97\,\mathrm{nm} undergoes 3rd order reflection at a Bragg angle of 60^\circ. Consider that the two beams are reflected from the same set of planes. Find the value of \lambda_1.
When a voltage v_1 = + 40 \mu\text{V} is applied to the non-inverting input terminal and a voltage v_2 = - 40 \mu\text{V} is applied to the inverting input terminal of an Op-Amp, an output voltage v_o = 100\text{ mV} is obtained. But, when v_1 = v_2 = + 40 \mu\text{V} is applied, one obtains v_o = 0\cdot 4\text{ mV}. Calculate the voltage gains for the difference and the common-mode signals, and the common-mode rejection ratio.
When is the channel of a JFET said to be pinched off ? Define the pinch-off voltage. Give the relationship between the pinch-off voltage, the saturation voltage and the gate-source voltage. Sketch the depletion region before and after pinch-off.