In an $LCR$ series circuit,if $V$ is the effective value of the applied voltage,$V_R$ is the voltage across $R$,and $V_L$ and $V_C$ are the effective voltages across $L$ and $C$ respectively,then:

If $L$ and $R$ are respectively the inductance and resistance,then the dimensions of $\frac{R}{L}$ will be

For a series $LCR$ circuit with $R=100\,\Omega$,$L=0.5\,mH$ and $C=0.1\,pF$ connected across $220\,V-50\,Hz$ $AC$ supply,the phase angle between current and supplied voltage and the nature of the circuit is:

The figure given below shows an $LCR$ series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed keeping $S_2$ open, the phase difference $(\phi)$ between the current and source voltage is $30^\circ$ and the phase difference is $60^\circ$ when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1 - L_2)$ is . . . . . . $H$.

In an $LR$ circuit of $3 \text{ mH}$ inductance and $4 \text{ } \Omega$ resistance,an $\text{emf } E = 4 \cos(1000t) \text{ V}$ is applied. The amplitude of the current is:

$A$ 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 $\omega/3$, the current becomes half of the original current. Then the ratio of capacitive reactance and resistance is