A variable capacitor is connected to a 200 V battery. If its capacitance is changed from 2 $$\mu$$F to X $$\mu$$F, the decrease in energy of the capacitor is 2 $$\times$$ 10^$$-$$2 J. The value of X is -

A potential difference of 200 V is maintained across a conductor of resistance 100 $$\Omega$$. The number of electrons passing through it in 1s is

The impedance of a series LCR circuit is -

When an alternating voltage E = E_o sin $$\omega$$t is applied to a circuit, a current $$I = {I_o}\sin \left( {\omega t + {\pi \over 2}} \right)$$ flows through it. The average power dissipated in the circuit is