Obtain an expression for the impedance of an LCR circuit for the following cases:

Write down the expression for the energy distribution of a black body radiation at temperature T and deduce. Wien's displacement law. \frac{h\omega_{m}}{kT} = \text{const.} Taking the constant to be equal to 3-\epsilon, where \epsilon is small (so that \epsilon can be neglected in comparison to 1). Find the value of \epsilon.

Calculate the power radiated by a tungsten filament 10 cm long and 0.010 mm in diameter, when it is heated to 2,500 K in an evacuated bulb. Assume that the filament radiates at 30% of the rate of a black body at the same temperature.

Two cells of emf 2 volts each and internal resistance 2 ohms rich are connected in parallel with each other and with a load resistance. Calculate the maximum power that can be dissipated in the load.

L and R in series and C in parallel to them.

L, C and R in series. Discuss the factors that determine sharpness of resonance in these cases.

Write a note on Physical significance of each of the four Maxwell's equation.