PYQ Bank

Implement the Boolean function X = AB + \bar{A}C using NAND gates.

Show that the reciprocal lattice for a ‘bcc’ lattice is a ‘fcc’ structure.

An n-p-n transistor with \beta = 49 is used in common-emitter amplifier mode with V_{cc} = 10\ \mathrm{V} and R_L = 2\mathrm{k}\Omega. If a 100\mathrm{k}\Omega resistor is connected between the collector and the base of the transistor, calculate the quiescent collector current. Assume V_{BE} = 0.

Calculate the pinch-off voltage for n-channel silicon FET with a channel width of 6 \times 10^{-4}\ \mathrm{cm} and a donor concentration of 10^{15}\ \mathrm{cm}^{-3}. Given that dielectric constant of silicon is 12.

A solid contains a dilute concentration of \mathrm{Nd}^{3+} ions, each of which possess three 4f electrons. Assuming that there are 10^{25}\ \mathrm{m}^{-3} of these ions, calculate the magnetic susceptibility of the sample at 1\,\mathrm{K}.

\questiondiagram{
} Sketch the dc load line for the circuit shown.

Consider atoms as hard, uniform spheres and packed closely together so that they fold touch one another. Calculate the number of atoms per cubic unit cell and fraction of volume occupied for simple cubic, body-centred and face-centred cubic structures.

What is an intrinsic semiconductor? Intrinsic silicon has a band gap of 1.1\,\mathrm{eV} and yet at T=300\,\mathrm{K}, the conductivity is non-zero. Explain. Comment, with the help of relevant expression, on the position of the Fermi level of an intrinsic semiconductor.

In an almost pure thick aluminium sheet, there are 0.19 atomic percent of copper at the surface and 0.18 atomic percent at a depth of 1.2\,\mathrm{mm} from the surface. Calculate the flux of the copper atoms from the surface at 550^\circ\mathrm{C}, if the diffusion coefficient of copper in aluminium at this temperature is 5.25 \times 10^{-13}\,\mathrm{m^2\,s^{-1}}. Given, Al FCC with lattice parameter, a = 4.05\,\mathring{\mathrm{A}}.

The lattice parameter and the atomic mass of a diamond crystal are 3.57\,\mathring{\mathrm{A}} and 12, respectively. Calculate the density of the crystal. Given, Avogadro's number, N = 6.023 \times 10^{26}\,(\mathrm{kg\ mol})^{-1}.

What is Josephson Effect ? Give an account of applications of superconductivity.

What is Meissner Effect ? Explain the validity of Meissner Effect in Type I and Type II superconductors.

Verify the following Boolean identities : (i) A + \bar{A} B = A + B (ii) \overline{\bar{A} + B} + \overline{\bar{A} + \bar{B}} = A

Describe the basic segments of a microprocessor and briefly mention their functions. Mention the name of widely used 8-bit microprocessors.

Consider an amplifier with an open-loop (no feedback) gain of A and a feedback factor \beta. Derive the expression for the gain with feedback, A_f. Derive the condition for the amplifier with feedback to act as an oscillator. Comment on the change in A_f with a change in A.

A transistor operating in the CE mode draws a constant base current \text{I}_{\text{B}} of 30\ \mu\text{A}. The collector current \text{I}_{\text{C}} is found to change from 3\cdot 5\text{ mA} to 3\cdot 7\text{ mA} when the collector-emitter voltage \text{V}_{\text{CE}} changes from 7\cdot 5\text{ V} to 12\cdot 5\text{ V}. Calculate the output resistance and \beta at \text{V}_{\text{CE}} = 12\cdot 5\text{ V}. What is the value of \alpha ?

Describe briefly the construction of an n-channel JFET. Define the pinch-off voltage and pinch-off current. Give the relationship between the pinch-off voltage, the saturation voltage and gate-source voltage.

The angles between the tetrahedral bonds of diamond are the same as the angles between the body diagonals of a stack of neighbouring cubes having common edges and not faces. Use vector analysis to find the value of the angle.

Deduce the Miller indices of the close-packed planes of atoms in the f.c.c. lattice.

A superconducting material has a critical temperature of 3\cdot 7~\text{K} and a magnetic field of 0\cdot 0306~\text{tesla} at 0~\text{K}. Find the critical field at 2~\text{K}.