An LC circuit a 20 mH inductor and a \(50\mu F\) capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.
(a) What is the total energy stored initially? IS it conserved during LC oscillations?
(b) What is the natural frequency of the circuit?
(c)  At what time is the energy stored 
(i) completely electrical (i.e., stored in the capacitor)?
(ii) completely magnetic (i.e., stored in the inductor).
(d) At what times is the total energy shared equally between the inductor and the capacitor?
(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

Consider an infinitely long wire carrying a current I (t), with \(\frac { dI }{ dt } =\lambda =constant.\) Find the current produced in the rectangular loop of wire ABCD if its resistance is R

A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle \(\theta \) with respect to the horizontal. The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.

State Lenz's law and illustrate it with experiment.

What is the difference between electric field produced by stationary charges and moving charges?

What are conservative and non-conservative fields?

Derive an expression for average power in an A.C. circuit containing resistor only.

A resistor of \(400\Omega \) an inductor of \(\frac { 5 }{ \pi H } \)and a capacitor of \(\frac { 50 }{ \pi } \mu F\) are connected in series across a source of alternating voltage of 140 \(sin\ \pi t\ V\). Find the voltage (rms) across the resistor, the inductor and the capacitor. Is the algebraic sum of these voltage more than the source voltage? If yes, resolve the paradox.

Draw a schematic diagram of a step-up transformer. Explain its working principle. Deduce the expression for the secondary to primary voltage in terms of the number of turns in the two coils. In an ideal transformer, how is this ratio related to the current in the two coils ?
How is the transformer used in large scale transmission and distribution of electrical energy over long distances ?