$A$ rejector circuit is the resonant circuit in which

$A$ capacitor and an inductance coil are connected in separate $AC$ circuits with a bulb glowing in both the circuits. The bulb glows more brightly when

Obtain an analytical solution for the relation of phase between instantaneous current and voltage for an $LCR$ series $AC$ circuit.

When the $rms$ voltages $V_L, V_C$ and $V_R$ are measured respectively across the inductor $L$,the capacitor $C$ and the resistor $R$ in a series $LCR$ circuit connected to an $AC$ source,it is found that the ratio $V_L : V_C : V_R = 1 : 2 : 3$. If the $rms$ voltage of the $AC$ source is $100 \, V$,the $V_R$ is close to........$V$

$A$ series $R-L-C$ circuit consists of an $8.0\ \Omega$ resistor,a $5.0\ \mu F$ capacitor,and a $50.0\ mH$ inductor. $A$ variable frequency source applies an $emf$ of $400\ V\ (rms)$ across the combination. The power delivered to the circuit when the frequency is equal to one-half the resonance frequency is.....$W$

Consider the parallel $LCR$ circuit shown in the figure. Find the net current $i$ and the phase of $i$. Show that $i = \frac{V}{Z}$. Find the impedance $Z$ for this circuit.