A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; It is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :

A fully charged capacitor $$C$$ with initial charge $${q_0}$$ is connected to a coil of self inductance $$L$$ at $$t=0.$$ The time at which the energy is stored equally between the electric and the magnetic fields is :

A boat is moving due east in a region where the earth's magnetic fields is $$5.0 \times {10^{ - 5}}$$ $$N{A^{ - 1}}\,{m^{ - 1}}$$ due north and horizontal. The best carries a vertical aerial $$2$$ $$m$$ long. If the speed of the boat is $$1.50\,m{s^{ - 1}},$$ the magnitude of the induced $$emf$$ in the wire of aerial is :

In a series $$LCR$$ circuit $$R = 200\Omega $$ and the voltage and the frequency of the main supply is $$220V$$ and $$50$$ $$Hz$$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $${30^ \circ }.$$ On taking out the inductor from the circuit the current leads the voltage by $${30^ \circ }.$$ The power dissipated in the $$LCR$$ circuit is