The primary of a transformer has 400 turns while the secondary has 2000 turns. If the power output from the secondary at 1000 V is 12 kW . The resistance of the primary is $0.2 \Omega$ and that of the secondary is $2 \Omega$. If the efficiency of the transformer is $80 \%$, then the power loss in the primary is

The alternating current in a circuit is given by $$I=50 \sin 314 t$$. The peak value and frequency of the current are

A $$50 \mathrm{~Hz}$$ $$\mathrm{AC}$$ signal is applied in a circuit of inductance of $$(1 / \pi) \mathrm{H}$$ and resistance $$2100 \Omega$$. The impedance offered by the circuit is

If the alternating current $$I=I_1 \cos \omega t+ I_2 \sin \omega t$$ then the rms current is given by