UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Show that FCC-crystals are more closely packed than BCC-crystals,

Give the Boolean expression and the truth table for an XOR gate. Why are NAND gates called universal gates ? Realise OR and XOR gates employing only NAND gates.

Simplify the equation: Y = [A \bar{B} (C + BD) + \bar{A} B C] using Boolean algebra. Give the logic circuit for the equation before and after the simplification.

Draw the device structure of a p-n junction solar cell and explain how the light energy is converted into electrical energy. Define the 'short-circuit current', open-circuit voltage' and 'efficiency' of a solar cell.

Explain the working of a phase-shift oscillator. Draw the circuit diagram of a phase-shift oscillator using either a transistor or an op-amp. What are the conditions which must be satisfied to achieve stable oscillations ? Calculate the frequency of oscillations for R = 10\ \Omega and C = 0.01\ \mu\text{F}.

Explain the difference between n-p-n and p-n-p transistors. Give their device structure and biasing circuits. Draw a circuit for a single-stage common-emitter amplifier.

Discuss briefly the concept of effective mass in semiconductors and explain the significance of negative effective mass.

What is Josephson effect? Discuss briefly DC and AC effects. Give some practical applications of Josephson junctions.

Show that a lattice cannot have a five-fold rotational symmetry. However, some solids appear to exhibit this rotational symmetry. Explain briefly how this can be done.

(i) Simplify the logical expression f = ABC + B \overline{C} D + \overline{A} BC by using Karnaugh map and realise f using NAND gates only. 10 (ii) The transistor in the following circuit has \beta = 100 and V_A = 90\text{ V}. What value of R_B will give 0 volt d.c. output 10

The following common-emitter amplifier is required to have a signal voltage gain V_{\text{out}} / V_S of at least 100. The transistor has \beta = 63, early voltage V_A = 100\text{ V} and I_{SE} = 1.5 \times 10^{-14}\text{ A} :

Assuming that the operating collector voltage is supposed to be + 6\text{ V}, perform related calculations to check whether the circuit satisfies the operating point and voltage gain criteria. The reactance of the capacitors can be neglected at all frequencies.

What are Brillouin zones ? How are they related to the energy levels of an electron in a metal ? Draw the Brillouin zone for a rectangular lattice of sides \pi and 2\pi. Also compute the energy at the corner and midpoints of the adjacent sides of the first Brillouin zone.

Explain the working and applications of a FET.

What is a microprocessor ? Explain the internal architecture of an 8085 \mu\text{P}.

(ii)

An In As semiconductor sample is cut in the form of a small bar of size 1 \cdot 0 \text{ cm} \times 1 \cdot 0 \text{ cm} \times 2 \cdot 0 \text{ mm}. Its lengthwise resistance is 1 \cdot 25 \ \Omega. A Hall field of 1 \cdot 7 \text{ V/m} develops when a current of 0 \cdot 12 \text{ A} is passed lengthwise and a magnetic field of 0 \cdot 05 \text{ T} is applied normal to its length as shown above. Calculate the carrier density. (iii) Determines the reciprocal lattice vectors of an fcc lattice.

Discuss the functioning of the above oscillator circuit. Obtain the condition for maintenance of oscillations and the expression for the frequency assuming that the resistances of the inductors are negligible.

Define (i) input bias current, (ii) input offset current, (iii) input offset voltage, (iv) output offset voltage, (v) power supply rejection ratio and (vi) slew rate for an OPAMP.

Draw the logic circuit for the following Boolean expression : Y = \overline{A + B} + \overline{C} What are the 'Y' values for the input combinations : (1) 1, 1, 0; (2) 1, 0, 1; (3) 0, 0, 1 ? (ii)

Define \alpha and \beta parameters of a transistor. A germanium transistor with \beta = 45 is biased as shown above. Calculate the value of R_b.

Discuss the motion of an electron in one-dimensional periodic potential and show that it leads to formation of bands of allowed and forbidden states in the electron energy spectrum. How are the insulators, semi-conductors and conductors discriminated on the basis of band structure ?

(i) Discuss briefly the concept of effective mass in semiconductors and explain the significance of negative effective mass. (ii) In isolated atoms, the electrons have discrete and definite energies but in solids they have bands of energies. Explain why. (iii) A proton, deuteron and \alpha-particle accelerated through the same potential difference, on entering a region of uniform magnetic field applied normal to their plane of motion, move in circular orbits. Compare the radii of the orbits described by them.