A coil of inductive reactance $\frac{1}{\sqrt{3}} \Omega$ and a resistance $1 \Omega$ are connected in series to a $200 \mathrm{~V}, 50 \mathrm{~Hz}$ AC source. The time lag between voltage and current is

An AC source of internal resistance $10^3 \Omega$ is connected to a transformer. The ratio of the number of turns in the primary to the number of turns in the secondary to match the source to a load resistance of $10 \Omega$ is

In a series LCR circuit, the voltages across the capacitor, resistor and inductor are in the ratio $2: 3: 6,$ if the voltage of the AC source in the circuit is 240 V , then the voltage across the inductor is

If the voltage and current in an AC circuit are respectively $50 \sin (50 t) \mathrm{V}$ and $50 \sin \left(50 t+\frac{\pi}{4}\right) \mathrm{mA}$, then the power dissipated in the circuit is nearly