An alternating current of frequency $f$ is flowing in a circuit containing a resistance $R$ and a choke $L$ in series. The impedance of this circuit is

When an $AC$ source of $e.m.f.$ $e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f.$ $e$ and the current $i$ in the circuit is observed to be $\pi/4$,as shown in the diagram. If the circuit consists possibly only of $RC$ or $LC$ in series,find the relationship between the two elements.

An e.m.f. $E=4 \cos (1000 t)$ volt is applied to an $LR$ circuit of inductance $3 \ mH$ and resistance $4 \ \Omega$. The maximum current in the circuit is

An inductor of inductance $L$ and resistor $R$ are joined together in series and connected to a source of frequency $\omega$. The power dissipated in the circuit is

$A$ circuit is made of $1 \Omega$ resistance and $2.5 \text{ mH}$ inductance in series. If an alternating source of $200 \text{ V}$ and $50 \text{ Hz}$ is connected to the circuit,then the phase difference between current and voltage is . . . . . . .

An a.c. voltage source $V=V_0 \sin \omega t$ is connected across resistance $R$ and capacitance $C$ in series. It is given that $R=\frac{1}{\omega C}$ and the peak current is $I_0$. If the angular frequency of the voltage source is changed to $\frac{\omega}{\sqrt{3}}$,then the new peak current in the circuit is