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

The time constant of the given $LR$ circuit is $\tau$. If the battery is replaced by an $AC$ source having voltage $V = V_0 \cos \omega t$,the power factor of the circuit will be

$A$ sinusoidal voltage of peak value $283 \, V$ and angular frequency $320 \, rad/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega$,$L = 25 \, mH$,and $C = 1000 \, \mu F$. The total impedance and the phase difference between the voltage across the source and the current will respectively be:

If the power factor is $1/2$ in a series $RL$ circuit with $R = 100\,\Omega$ connected to an $ac$ mains $(50\,Hz)$,find the value of $L$.

In an $LR$ circuit,the value of $L$ is $(\frac{0.3}{\pi}) \ H$ and the value of $R$ is $40 \ \Omega$. If an alternating e.m.f. of $230 \ V$ at $50 \ Hz$ is connected to the circuit,what are the impedance and the current in the circuit,respectively?

The phase difference between the alternating current and emf is $\frac{\pi}{2}$. Which of the following cannot be the constituent of the circuit?