An inductor and a resistor are connected in series to an AC source of voltage $144 \sin \left(100 \pi t+\frac{\pi}{2}\right) \mathrm{V}$. If the current in the circuit is $6 \sin \left(100 \pi t+\frac{\pi}{6}\right) \mathrm{A}$, then the resistance of the resistor is

A resistance of $20 \Omega$ is connected to a source of an alternating potential $V=200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value, then $t$ is (in seconds)

A full wave rectifier circuit is operating from 50 Hz mains. The fundamental frequency in the ripple output will be

A series $L-C-R$ circuit is shown in the figure. Where the inductance of 10 H , capacitance $40 \mu \mathrm{~F}$ and resistance $60 \Omega$ are connected to a variable frequency 240 V source. The current at resonating frequency is