In a given series $LCR$ circuit,$R = 4\, \Omega, X_L = 5\, \Omega$ and $X_C = 8\, \Omega$. The current :-

In an $LC$ circuit,the inductance $L = 40 \; mH$ and capacitance $C = 100 \; \mu F$. If a voltage $V(t) = 10 \sin (314 t)$ is applied to the circuit,the current in the circuit is given by:

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 $L$.

$A$ resistance of $300 \ \Omega$ and an inductance of $\frac{1}{\pi} \ H$ are connected in series to an $AC$ voltage of $20 \ V$ and $200 \ Hz$ frequency. The phase angle between the voltage and current is

An inductor and a resistor in series are connected to an $A.C.$ supply of variable frequency. As the frequency of the source is increased,the phase angle between current and the potential difference across $L$ will

$A$ series combination of resistor $R$ and capacitor $C$ is connected to an $A$.$C$. source of angular frequency $\omega$. Keeping the voltage same,if the frequency is changed to $\frac{\omega}{3}$,the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is