A series LCR circuit with \mathrm{L} = 2\text{ H}, \mathrm{C} = 2\text{ }\mu\text{F} and \mathrm{R} = 20\\ \Omega is powered by a source of 100\text{ volts} and variable frequency. Find
(i) the resonance frequency, f_0,
(ii) the value of Q
(iii) the width of resonance \Delta f and
(iv) the maximum current at resonance.
A Geiger tube consists of a wire a wire of radius 0.2\text{ mm} and length 12\text{ cm} and a co-axial metallic cylinder of radius 1.5\text{ cm} and length 12\text{ cm}. Find
(i) the capacitance of the system, and
(ii) the charge per unit length of the wire when the potential difference between the wire and the cylinder is 1.2\text{ kV}. (Assume the dielectric constant of the gas in the tube to be 1)
Show that the potential energy of a charge Q uniformly distributed throughout the sphere of radius R is given by PE = \frac{3}{5} \frac{Q^2}{4\pi\varepsilon_0 R}
Calculate the electric field for a point on the axis of a uniform ring of a charge 'q' and radius a. Show that the maximum value occur at x = \pm a/2.
A wave is represented by \Psi_1 = 10 \cos(5x - 25t). Find wavelength \lambda, velocity v, frequency f and the direction of propagation. If it interferes with another was given by \psi_2 = 20 \cos(5x + 25t + \pi/3), find the amplitude and the phase of the resultant wave. (All dimensions are in SI system).
Show that the motion of a classical particle is analogous to the motion of a wave packet, which can be constructed by superposition of a large number of plane waves. Construct such a wave packet and derive an expression for its group velocity.
How do you know that the light is a transverse wave? What is a quarter wave plate? How is it constructed?
Discuss the Fresnel diffraction pattern formed by a straight edge using the Cornu's spiral.
Derive the expression for resolving power of a diffraction grating with N lines. Calculate the minimum number of lines in the diffraction grating if it has to resolve the yellow lines of sodium (589.0\text{ nm} and 589.6\text{ nm}) in the first order.
In an experiment using a Michelson interferometer, explain with the help of suitable ray diagrams.
(i) Why do we need extended source of light,
(ii) Why do we get circular fringes, and
(iii) Shifting of fringes inwards or outwards as we shift the movable mirror.
State Fermat's principle. Apply it to get the laws of reflection from a plane surface.
The phase velocity of the surface wave in a liquid of surface tension T and density \rho is given by u_p = \sqrt{\frac{g\lambda}{2\pi} + \frac{2\pi T}{\lambda\rho}} Show that the group velocity u_g of the surface wave is given by u_g = \frac{g + (12\pi^2 T) / \rho\lambda^2}{2\sqrt{\left(\frac{2\pi g}{\lambda} + \frac{8\pi^3 T}{\rho\lambda^3}\right)}}
Derive the relationship between the impact parameter and the scattering angle for the scattering of an particle of charge +2e by a nucleus of charge +Ze. Calculate the impact parameter for an angle of deflection of 30^\circ if the kinetic energy of the alpha particle is 6 \times 10^{-13}\text{ J}.
Using the rocket equation and its integral find the final velocity of a single stage rocket. Given that
(i) the velocity of the escaping gas is 2500\text{ m/s},
(ii) the rate of loss of mass is. (where m_0) is the initial mass and 0.27 m_0 is the final mass).
An observer A sees two events at the same space point (\Delta x = \Delta y = \Delta z = 0) and separated in time by \Delta t = 10^{-6}\text{ s}. Another observer B sees them to be separated by \Delta t' = 3 \times 10^{-6}\text{ s}. What is the separation in space of the two events as observed by B? What is the speed of B relative to A?
Two spaceships are moving at a velocity of 0.9\text{ c} relative to the Earth in opposite directions. What is the speed of one spaceship relative to the other? (c = \text{velocity of light})
Using the Lagrangian for the system of a planet and the Sun obtain the equation of motion. Use them to get the equations for the orbit.
(i) FETs have unique properties which make BJTs not suitable for some important applications. What are these most important FET applications? (ii) Briefly describe FETs as variable resistors.
(i) Obtain reciprocal lattice to normal BCC lattice. (ii) Describe Josephson junction and the effect. How is it exploited in the formation of a SQUID? Write down the applications of a SQUID. (iii) Distinguish between intrinsic and extrinsic semiconductors. Explain the concept of hole.
(i) What are sequential switching circuits (ii) Describe a simple sequential circuit. (iii) Describe a clocked RS Flip-Flop, (iv) Briefly describe ROMs.
