PYQ Bank

Calculate the critical temperature for helium, given the values for critical constants, a = 6.15 \times 10^{-5}, b = 9.95 \times 10^{-4}, where the unit of pressure is atm and the sample is kept at NTP.

A reversible engine converts 1/6 of the heat input into work. When the temperature of the sink is reduced by 62\ ^{\circ}\mathrm{C}, its efficiency is doubled. Find the temperatures of source and sink.

Describe neutron star on the basis of Fermi-Dirac statistics and obtain the condition of critical mass for a neutron star.

Derive Clausius-Clapeyron equation. How does it explain the effect of pressure on melting point of solids and boiling point of liquids?

Prove the thermodynamic relation : \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V and hence show that \frac{\mathrm{d}P}{\mathrm{d}T} = \frac{L}{T (V_2 - V_1)} ; all the terms have their usual meanings.

1 litre of hydrogen at 127^{\circ}\mathrm{C} and 10^{6} dynes \mathrm{/cm}^{2} pressure expands isothermally until its volume is doubled and then expands adiabatically until its volume is redoubled. Calculate the resulting pressure. \gamma = 1.42

Write down the electromagnetic wave equations in non-conducting dielectric medium. Hence show that the velocity of wave propagation is given by v=\sqrt{\frac{1}{\varepsilon\mu}}, where the symbols have their usual meanings.

Write down Stefan-Boltzmann law of radiation and derive it from Planck's law of radiation. An aluminium foil of relative emittance 0.1 is placed between two concentric spheres (assumed perfectly black) at temperatures 300\,\mathrm{K} and 200\,\mathrm{K} respectively. Find the temperature of the foil once the steady state is reached.

Discuss the reflection and refraction of plane electromagnetic waves at plane dielectric boundaries for normal incidence and also find the reflection and transmission coefficients.

Write down the physical significance of Maxwell's equations and explain the concept of displacement current by using a proper example.

(i) Using Maxwell's equations, obtain the relation \frac{1}{c} \frac{\partial}{\partial t} \left( \frac{E^2 + B^2}{2} \right) + \vec{\nabla} \cdot (\vec{E} \times \vec{B}) = 0 (ii) What is Poynting vector ? Deduce Poynting theorem for the flow of energy in an electromagnetic field.

How does one explain the observed spectrum of black-body radiation using Planck's quantum hypothesis ? State and obtain Wien's displacement law. Also explain the important features of this law.

Write down the four Maxwell's equations and explain the contribution of Maxwell in the development of these equations.

(i) Define and explain the significance of the quality factor of an electrical machine. (ii) Discuss in brief, the working principle of a transformer.

(i) State Faraday's law of electromagnetic induction and prove that it can be expressed in the following vector form : \mathrm{Curl}~\vec{E} = -\frac{\partial \vec{B}}{\partial t} with \vec{E} and \vec{B} being the electric and magnetic fields. (ii) A coil of 10 turns has dimension 9~\text{cm} \times 7~\text{cm}. It rotates at the rate of 15\pi~\text{rad/sec} in a uniform field whose flux density is 0\cdot 6~\text{weber/m}^2. What is the maximum e.m.f. induced in the coil ?

Use the method of electric images to find the electric field on the surface of a grounded conducting sphere.

State and explain the Biot-Savart law. Derive an expression for the magnetic field at a point due to an infinitely long straight current carrying conductor.

In a one-dimensional device, the charge density is given by \rho_V = \rho_0 \frac{x}{a}. If E = 0 at x = 0 and V = 0 at x = a, find V and E using Laplace equation of electrostatics.

When a person carrying something metallic walks through the doorway of a metal detector, it emits a sound. Explain the reason behind it. A 200\Omega resistor and a 15\mu\mathrm{F} capacitor are connected in series to 220 V, 50 Hz a.c. supply. Calculate the current in the circuit and the r.m.s. voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the supply voltage? If yes, resolve the paradox.

How large an inductance needs to be connected in series with a 120 V, 60 W lightbulb if it is to operate normally when the combination is connected across a 240 V, 60 Hz supply?