$A$ 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 alternating current source of frequency $100\, Hz$ is connected to a combination of a resistor,a capacitor,and an inductor in series. The potential difference across the inductor,the resistor,and the capacitor is $46\, V$,$8\, V$,and $40\, V$ respectively. The electromotive force $(EMF)$ of the alternating current source in volts is:

For the given $RL$ circuit,the maximum power loss across the circuit can be $W$.

In an $LCR$ series circuit,if ${X_C} < {X_L}$ and ${X_C} > {X_L}$,determine whether the current in the circuit leads or lags the voltage.

An $AC$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\omega/3$ (maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

When $100\, V$ $DC$ is applied across a solenoid,a current of $1\, A$ flows in it. When $100\, V$ $AC$ is applied across the same coil,the current drops to $0.5\, A$. If the frequency of the $AC$ source is $50\, Hz$,the impedance and inductance of the solenoid are: