$A$ 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

An $A.C.$ circuit contains a resistance of $12 \ \Omega$ and an inductive reactance of $5 \ \Omega$. The phase angle between the current and the potential difference will be

Switch $S$ is closed at $t = 0$. After a sufficiently long time,an iron rod is inserted into the inductor $L$. Then,the light bulb:

$A$ resistance $R$ draws power $P$ when connected to an $AC$ source. If an inductance is now placed in series with the resistance,such that the impedance of the circuit becomes $Z$,the power drawn will be

For the $AC$ circuit shown below,the phase difference between emf and current is $\frac{\pi}{4}$ radian as shown in the graph. If the impedance of the circuit is $1414 \Omega$,then the values of $P$ and $Q$ are

An ideal choke draws a current of $8 \, A$ when connected to an $AC$ supply of $100 \, V, 50 \, Hz$. $A$ pure resistor draws a current of $10 \, A$ when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the $AC$ source of $150 \, V, 40 \, Hz$. The current in the circuit becomes