An inductor and a resistor are connected in series to an $AC$ source. The current in the circuit is $500 \,mA$, if the applied $AC$ voltage is $8 \sqrt{2} \,V$ at a frequency of $\frac{175}{\pi} \,Hz$, and the current in the circuit is $400 \,mA$, if the same $AC$ voltage at a frequency of $\frac{225}{\pi} \,Hz$ is applied. The values of the inductance and the resistance are respectively:

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 the given circuit,the $rms$ value of current $(I_{rms})$ through the resistor $R$ is: $..........\,A$

$A$ circuit containing an $80 \, mH$ inductor and a $60 \, \mu F$ capacitor in series is connected to a $230 \, V, 50 \, Hz$ supply. The resistance of the circuit is negligible.
$(a)$ Obtain the current amplitude and $rms$ values.
$(b)$ Obtain the $rms$ values of potential drops across each element.
$(c)$ What is the average power transferred to the inductor?
$(d)$ What is the average power transferred to the capacitor?
$(e)$ What is the total average power absorbed by the circuit? ('Average' implies 'averaged over one cycle'.)

In a series $L-C-R$ circuit,the frequency of a $10 \, V$ $a.c.$ voltage source is adjusted in such a fashion that the reactance of the inductor measures $15 \, \Omega$ and that of the capacitor $11 \, \Omega$. If $R = 3 \, \Omega$,the potential difference across the series combination of $L$ and $C$ will be.....$V$.

In a series $L-C-R$ circuit,