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

In a series resonant LCR circuit, for the power dissipated to become half of the maximum power dissipated, the current amplitude is

If a resistor of resistance $4 \Omega$, a capacitor of capacitive reactance $6 \Omega$ and an inductor of inductive reactance $9 \Omega$ are connected in series with an AC source, then the impedance of the circuit is

A resistor of $450 \Omega$ and an inductor are connected in series to an AC source of frequency $\frac{75}{\pi} \mathrm{~Hz}$. If the power factor of the circuit is 0.6 , then the inductance connected in the circuit is