Define quality factor for an A.C. circular and discuss the meaning of electrical resonance in a series LCR circuit. Explain the term sharpness of resonance.

Determine the energy of attraction between an electric dipole and a plane conducting surface at zero potential.

Obtain the characteristic impedance of the vacuum. Derive the expression used.

Derive the distribution law which explains the black body spectrum over the entire wavelength region. Using this relation determine the value of Wiens constant b.

An alternating voltage, v = V_0 \sin (\omega t + \phi) is applied to a series RL circuit through a switch. Find the sum total of the transient and steady currents. Find the conditions when transient current becomes

(i) zero, and

(ii) maximum

The self inductance of primary and secondary coils of a R.F. transformer is 10\text{ mH} each. When the coils are connected in series self resonating frequencies are 132.6\text{ kHz} and 108.3\text{ kHz}. Calculate the mutual inductance between the coils and the winding capacitance.

Calculate the magnetic moment of a coil having 100 turns, each of area 10\text{ cm}^2 carrying a current of 1\text{ mA}, flowing for 1\text{ ms}. The coil is placed in a magnetic field of 0.5\text{ kg} which is perpendicular to the magnetic moment. Calculate the torque acting on the coil and the angular momentum transferred to it.

Using Gauss law find the electric field inside a cylindrical capacitor and hence derive the expression for its capacitance. Find the dielectric constant of the material inside a 50\text{ mm} long capacitor of capacitance 40\ \mu\text{F} having inner conductor of radius 1\text{ mm}, outer conductor of radius 10\text{ mm}. Which of the materials has such a value of the dielectric constant ?

Write down Maxwell's equations in free space and hence show that the phase velocity of the electromagnetic wave is equal to the velocity of light in free space.

Show that electromagnetic propagating in a homogeneous isotropic medium, arc transverse in nature.

Show that attenuation constant \alpha and phase factor \beta for an electromagnetic wave, propagating in a perfectly conducting medium, are equal. At what frequency the skin depth in silver is 1\ \mu\text{m} when the conductivity of silver is 30 \times 10^6\text{ Siemens/meter} and relative permeability is 1.0?

An electric dipole moment, \vec{p}_2, is placed at (r, \theta) in he electric field of another dipole moment \vec{p}_1, placed at he origin. Assuming that the electric potential, V, at (r, \theta) due to \vec{p}_1 is V(r, \theta) = \frac{p_1 \cos \theta}{4 \pi \epsilon_0 r^2} find the dipole-dipole interaction energy.

An alternating voltage is applied to the circuit shown in Fig. 1. Show that it has two resonant frequencies, f_p and f_s interrelated as f_p = f_s \sqrt{\left(1 + \frac{1}{r}\right)} Where r = \left(\frac{C_b}{C_a}\right)

Starting from Biot Savart's law, find the vector potential at a distance r, from a current carrying wire.

A relay has a coil resistance of 10\ \Omega and inductance of 1\text{ H}. It is energized by a single voltage pulse of 10\text{ V} which remains constant for 250\text{ ms} and then falls to 0\text{ V}. Relay contact closes when the increasing current reaches 200\text{ mA} and opens when the decreasing current is at 100\text{ mA}. Calculate the time for which the relay contact is closed.

Self inductance of two coils, A and B, connected in series is 25\text{ mH} or 10\text{ mH}, depending on the relative current directions in the coils. Self inductance of the isolated coil. A, is 10\text{ mH}. Calculate mutual inductance M of the pair of coils coupling factor and leakage factor. If the current in coils is changing at the rate of 1000\text{ A/s}, find the induced electromotive forces across the coil A.

Write a short note on Solar constant.

An alternating voltage of varying frequency is applied across a two-branch parallel circuit of R_1 and L in series and R_2 and C in series as shown in Fig. below.

Find its resonant frequency. If R_1 and R_2 are not zero, state the conditions when the resonant frequency is given by f_0 = \frac{1}{2\pi \sqrt{LC}}

An alternating voltage is applied to CR circuit connected in series. Under what conditions it acts as an (i) integrator and (ii) a differentiator?

An electric dipole is placed in an external electric field. Find the interaction energy between the electric dipole and the field. And hence find the force and the torque acting on the dipole.