$A$ series $R-C$ combination is connected to an $AC$ voltage of angular frequency $\omega = 500 \ rad/s$. If the impedance of the $R-C$ circuit is $R\sqrt{1.25}$,the time constant (in $ms$) of the circuit is:

$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be-

$A$ resistor and an inductor are connected in series to an $AC$ source of voltage $V = 150 \sin (100 \pi t + \pi) \text{ V}$. If the current in the circuit is $I = 5 \sin (100 \pi t + \frac{2 \pi}{3}) \text{ A}$,then the average power dissipated and the resistance of the resistor are respectively:

$A$ series $L, R$ circuit connected with an ac source $E = (25 \sin 1000 t) \ V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E = (20 \sin 2000 t) \ V$,the new power factor of the circuit will be:

$A$ sinusoidal voltage $V_0 \sin \omega t$ is applied across a series combination of resistance $R$ and inductance $L$. The amplitude of the current in this circuit is

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is