A series $\mathrm{LCR}$ circuit is shown in the figure. If inductor is removed from the circuit then current leads the voltage by $45°$ while if the capacitor is removed then the current lags the voltage by $45°$. The rms current in the original$\mathrm{LCR}$ circuit is

Switch is in position $A$ for a long time. At time $0$, it is switched to position $B.$ Find time period of resulting charge oscillation.

$\mathrm{STATEMENT};-1 :$A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.

$\mathrm{STATEMENT}; - 2 :$ In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction

The potential difference $V$ across and the current $I$ flowing through an instrument in an AC circuit are given by 

$V=5\cos \omega t \mathrm{V}$

$I=2\sin \omega t \mathrm{A}$

The power dissipated in the instrument is