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}.
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.
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.
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.
Show that the reciprocal lattice for a ‘bcc’ lattice is a ‘fcc’ structure.
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 Josephson Effect ? Give an account of applications of superconductivity.
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.
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}}.
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.
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.
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}.
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.
What is Meissner Effect ? Explain the validity of Meissner Effect in Type I and Type II superconductors.
A transistor having \alpha = 0\cdot 975 and a reverse saturation current I_{\text{CO}} = 10~\mu\text{A} is operated in CE configuration. What is \beta for this configuration? If the base current is 250~\mu\text{A}, calculate the emitter current and the collector current.
Describe briefly the construction of an enhancement type MOSFET using a p-type silicon bar. Point out the structural difference between enhancement and depletion forms of the MOSFET.
Obtain the Boolean expression for the output Y in the given logic circuit :
Simplify the expression and show that the circuit is equivalent to an AND gate with inputs A and B.
