Consider an energy band which is filled with electrons up to a certain value k_1 \left(k_1 < \frac{\pi}{a}\right). Determine the total effective number of free electrons in the energy band. Comment on the electron distribution in an insulator, intrinsic semiconductor and metals at 0\text{ K}. Symbols have their usual meanings.
(i) Explain the Bravais lattice and non-Bravais lattice with suitable diagram. (ii) Draw the (1\ 0\ 0), (1\ 1\ 0) and (1\ 1\ 1) planes in a cubic unit cell. (iii) Obtain the Miller indices of a plane with intercepts a, b/2, 3c in a simple cubic unit cell.
(i) How will you obtain OR gate from NAND gate? Draw the logic circuit for the following expressions : Y = ABC + \bar{D} Y = (\bar{E}G + B)H (ii) What is a thermistor? Explain the working of thermistor by drawing temperature-resistance curve.
What is Boolean algebra? State De Morgan's theorems and determine the output expressions for the circuit shown below by using De Morgan's theorems :
What is Josephson effect? How can Josephson junctions be used to produce macroscopic quantum interference?
What is a microprocessor? Briefly mention the basic units of a microprocessor by drawing descriptive block diagram of 8085 microprocessor.
What is an oscillator? Explain the Barkhausen criterion and working principle of an R-C phase-shift oscillator with suitable circuit diagram.
Describe the bandwidth and slew rate of an Op-Amp. The amplifier shown in the below circuit is used to amplify an input signal to a peak output voltage of 100\text{ mV} and its slew rate is 0\cdot 5\text{ V}/\mu\text{s}. What is the maximum operating frequency of the amplifier?
(i) Give a qualitative description of the BCS theory and explain how it accounts for the superconducting state. (ii) The critical field of niobium is 1 \times 10^5\text{ A/m} at 8\text{ K} and 2 \times 10^5\text{ A/m} at absolute zero. Find the transition temperature of the element.
State the Barkhausen criterion for sustained oscillations of a feedback circuit. Explain the operation of a Hartley oscillator using proper circuit diagram.
Consider the planes with indices (1\ 0\ 0) and (0\ 0\ 1); the lattice is f.c.c., and the indices refer to the conventional cubic cell. What are the indices of these planes when referred to the primitive axes : \vec{a}_1 = \frac{a}{2}(\hat{x}+\hat{y}), \vec{a}_2 = \frac{a}{2}(\hat{y}+\hat{z}) and \vec{a}_3 = \frac{a}{2}(\hat{z}+\hat{x})?
(i) Prove that \overline{AB + \bar{A} + AB} = 0.
The density of a liquid monovalent metal near absolute zero temperature is given to be 0\cdot 081\text{ g cm}^{-3}. Calculate the Fermi energy \varepsilon_F, the electron velocity v_F at the Fermi surface and the Fermi temperature T_F.
State the characteristics of an ideal Op-Amp. Explain the use of an Op-Amp as a summing amplifier and a differentiator.
Given that for intrinsic Si at T = 300\text{ K}, the band gap is 1\cdot 1\text{ eV} and the intrinsic carrier concentration is n_i = 1\cdot 5 \times 10^{10}\text{ cm}^{-3}. (i) Calculate the intrinsic carrier concentration at T = 450\text{ K}. Assume that the band gap at T = 450\text{ K} is 1\cdot 08\text{ eV}.
(ii) Recalculate the intrinsic carrier concentration at T = 450\text{ K} by assuming that the effective electron and hole masses in the respective bands decrease by 0\cdot 5\%.
(ii) Draw a simplified logic circuit for the following Boolean expression : Y = (A + B)\overline{AB}
The n\text{-}p\text{-}n transistor given below has \beta = 100, I_{CO} = 12\text{ nA} and V_{BE} = 0\cdot 8\text{ V}. Determine the transistor currents and the region of operation of the transistor. What happens if R_C is indefinitely increased?
Draw the crystal structure of \text{CaF}_2 indicating the positions of cations and anions. What are their respective coordination numbers?
Consider an n-channel JFET which has \text{I}_{\text{DSS}} = 15\text{ mA} and pinch-off voltage \text{V}_\text{p} = -5\text{ V}. If \text{V}_{\text{GS}} = -1\cdot 5\text{ V}, how much will the drain current \text{I}_\text{D} be? What will be the minimum value of \text{V}_{\text{DS}} for pinch-off to occur at \text{V}_{\text{GS}} = -1\cdot 5\text{ V}?