The impedance function of a parallel R, L and C circuit has poles loaded at - 3 \pm 4j\text{ radians/second}. If the value of \text{L} = 1\text{ Henry}, determine the following :
(i) The value of R and C.
(ii) What is the quality factor of this circuit ? Derive an expression for series and parallel circuit.
Write the Laplace's equation in Cartesian, spherical polar and cylindrical coordinates in one-dimensional space. Using a suitable Laplace's equation out of these three, find the capacitance of parallel plate capacitor.
Consider the two branch parallel circuit shown in the diagram. Determine the resonant frequency of the circuit.
Given an infinite line charge of charge density 2\,\mathrm{nC\,m^{-1}} parallel to the y-axis and passing through the point (3,0,4)\,\mathrm{m} and an infinite sheet of charge of charge density 4\,\mathrm{nC\,m^{-2}} parallel to the x-y plane and passing through the point (0,0,6)\,\mathrm{m}. Calculate the electric field intensity at the point (10,10,10)\,\mathrm{m}. Assume free space.
A rod of length l is perpendicular to a uniform magnetic field \mathrm{B}. The rod revolves at an angular speed \omega about an axis passing through one end of the rod and parallel to the magnetic field \mathrm{B}. Find the voltage induced across the rod's ends.
In the given circuit, L=2.0\,\mu\mathrm{H}, R=1.0\,\Omega, R_0=2.0\,\Omega and E=3.0\,\mathrm{V}. Find the amount of heat generated in the coil after the switch S is disconnected. The internal resistance of the source is negligible.
A body executes Simple Harmonic Motion such that its velocity at the mean position is 2\cdot 0\text{ m/s} and acceleration at one of the extremities is 1\cdot 57\text{ m/s}^2. Calculate the time period of vibration.
What are beats ? A tuning fork gives 6 beats per second with 25\cdot 4\text{ cm} length of stretched sonameter wire. The same 6 beats are heard per second when the length of the same wire is reduced to 24\cdot 6\text{ cm}. Calculate the frequency of the tuning fork.
What is damped harmonic oscillation? Write the equation of motion and obtain the general solution for this oscillation. Discuss the cases of dead beat, critical damping and oscillatory motion based on the general solution. What would be the logarithmic decrement of the damped vibrating system, if it has an initial amplitude 30\,\mathrm{cm}, which reduces to 3\,\mathrm{cm} after 20 complete oscillations?
A mass m is suspended by two springs having force constants k_1 and k_2 as shown in the figure. The mass m is displaced vertically downward and then released. If at any instant t, the displacement of the mass m is x, then show that the motion of the mass is simple harmonic motion having frequency f=\frac{1}{2\pi}\sqrt{\frac{1}{m}\left(\frac{k_1k_2}{k_1+k_2}\right)}
What is the principle of propagation in optical fibers ? Explain with the help of neat diagram, the ray propagation in Step index and Parabolic index optical fibers. How can pulse dispersion be minimized using Parabolic index optical fibers ?
A thin film of petrol of thickness 9 \times 10^{-6}\,\mathrm{cm} is viewed at an angle 30^\circ to the normal. Find the wavelength(s) of light in visible spectrum which can be viewed in the reflected light. The refractive index of the film \mu = 1.35.
Show that the phenomenon of Fraunhofer diffraction at two vertical slits is modulation of two terms viz. double slit interference and single slit diffraction. Obtain the condition for positions of maxima and minima.
In a step-index optical fiber system, explain the terms pulse dispersion and material dispersion. An optical fiber having refractive indices of core and cladding n_1 = 1.463 and n_2 = 1.444 respectively, uses a Laser diode with \lambda_0 = 1.50\,\mu\mathrm{m} with a spectral width of 2\,\mathrm{nm}. At this wavelength if the material dispersion coefficient, D_{m} is 18.23\,\mathrm{ps/(km\cdot nm)}, then calculate the pulse dispersion and material dispersion for 1\,\mathrm{km} length of the fiber.
Consider that a continuous laser beam which is assumed to be perfectly monochromatic with a wavelength of 6500\text{ \AA} is chopped into 2\text{ ns} pulses using a shutter. Calculate the number of photons in each pulse, if the power of each pulse is 5\text{ mW}.
A transparent film of glass of refractive index 1\cdot 5 is introduced normally in the path of one of the interfering beams of Michelson interferometer which is illuminated with light of wavelength 5893\text{ \AA}. This causes 500 dark fringes to shift across the field. Determine the thickness of the film.
Two glasses have dispersive powers in the ratio 2 : 3. These glasses are used in the manufacture of an achromatic contact objective of focal length 50\text{ cm}. What are the focal lengths of the lenses ?
What is achromatism ? Obtain the condition for achromatism of two thin lenses separated by a distance of x metres.
What is chromatic aberration? Obtain the condition for achromatism using combination of two thin lenses placed in contact to each other. Can this system work as achromatic doublet if both are of same material? Justify your answer.
What is the Resolving power of a grating ? Obtain an expression for the Resolving power of a grating, based on Rayleigh's criterion of resolution.