Find average power in electric circuit if source voltage (V) = 20sin(100wt) and current in the circuit (I) = 2sin(100wt + $\frac{\pi }{3}$ )

A circuit is made up of resistance 3 Ω and inductance 0.01 H. An alternating emf of 100 V at 50 Hz is connected, then the phase difference between the current and the emf in the circuit is

A radioactive sample decays by 63% of its initial value in 10s. It would have decayed by 50% of its initial value in :-

A coil has resistance of 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source of 200 V, 100 Hz is connected across the coil, current in coil will be

Two bodies of mass 10 kg and 2 kg are moving with velocities m/s and m/s respectively. The velocity of their centre of mass is

A capacitor having capacitance of 100 µF is charged with a potential difference of 12 V is connected to an inductor of inductance 10 mH. Find the maximum current through the inductor.