UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Construct an operational amplifier based analog computer to solve the differential equation \frac{d^2v}{dt^2}-\frac{dv}{dt}+2v=0.

What are the rules followed in biasing a bipolar junction transistor when it is used as an amplifier? Show how n-p-n and p-n-p transistors to be used as an amplifier are biased and the direction of flow of base, collector and emitter currents.

Starting from an expression for the group velocity, arrive at an expression for the effective mass of an electron in a semiconductor. Explain the significance of sign of the effective mass.

Describe the characteristic properties of a superconductor. Derive London equation for a superconductor and hence explain Meissner effect.

Find an expression for lattice specific heat of solids, and its low and high temperature limits. What is Debye temperature?

Distinguish between intrinsic and extrinsic semiconductors. Show that in a semiconductor, the product of concentrations of the two types of charge carriers is constant at a given temperature.

Draw the common-base amplifier circuit, using an n-p-n transistor and briefly discuss its working.

Simplify the logical expression \overline{(A+B)}B(A+\bar{C}) and draw the logical circuit to implement it.

Using OP-AMPs design an analog circuit to solve the following differential equation : \frac{d^2 v}{dt^2} + k_1 \frac{dv}{dt} + k_2 v = v_1(t) with \frac{dv_{(0)}}{dt} = 1\cdot 5\text{ V}; v_{(0)} = 2\cdot 0\text{ V}.

(i) What are intrinsic and extrinsic semiconductors ? Explain. (ii) How are n-type and p-type semiconductors obtained ?

Using band theory of solids, explain whether the effective mass of an electron can be positive, negative as well as infinity. Explain the significance of negative mass.

How are the band structures of insulators and semiconductors similar ? How are they different ?

Simplify the logical expression AB + \bar{A}\bar{B} + ABC using a Karnaugh map.

Explain the basic structure and operation of an n-channel FET. How FET acts as an amplifier ? Explain.

Derive Bragg diffraction condition in vectorial form using incident and diffracted wave vectors and reciprocal lattice vector.

An electron beam of 4 Kev is diffracted through a Bragg angle of 16^\circ for the first maxima. If the energy is increased to 16 keV, find the corresponding Bragg angle for diffraction.

Explain the origin of energy band formation in solids. Show that in nearly free electron approximation, the energy band gap is 2|V_G|, where V_G is Fourier transform of periodic potential seen by the valence electrons.

Show the variation of magnetization with applied magnetic field for type I and type II superconductors. Describe their behaviour. Discuss their potential for various applications.

Discuss the motion of an electron in an allowed energy band under the influence of an external electric field. Obtain an expression for the effective mass of the electron and discuss its variation in the band.

In one experiment, a perfect conductor and a superconductor are cooled to below 1\text{ K} and then a magnetic field is applied. In another experiment, they are cooled to below 1\text{ K} in magnetic field. Describe their responses in these two experiments and explain.