An $L-C-R$ series circuit is connected to an $AC$ source of peak voltage $240 \ V$. The phase difference between voltage and current of this circuit is $45^{\circ}$ and the resistance is $100 \ \Omega$. The $rms$ value of current through the circuit is . . . . . . . (in $A$)

$A$ series $LCR$ circuit consists of an inductor $L$,a capacitor $C$,and a resistor $R$ connected across a source of emf $\varepsilon = \varepsilon_0 \sin \omega t$. When $\omega L = \frac{1}{\omega C}$,the current in the circuit is $I_0$. If the angular frequency of the source is changed to $\omega^{\prime}$,the current in the circuit becomes $\frac{I_0}{2}$. Then,the value of $\left|\omega^{\prime} L - \frac{1}{\omega^{\prime} C}\right|$ is

As shown in the figure,a series circuit connected across a $200 \,V, 60 \,Hz$ line consists of a capacitor of capacitive reactance $X_C = 30 \,\Omega$,a non-inductive resistor of $R_1 = 44 \,\Omega$,and a coil of inductive reactance $X_L = 90 \,\Omega$ and resistance $R_2 = 36 \,\Omega$. The power dissipated in the coil is.....$W$

Obtain the relation of phase between instantaneous current and voltage with the help of a phasor diagram for a series $LCR$ circuit.

Write the differential equation of charge for $L-C-R$ series $AC$ circuit.

Which one of the following graphs correctly represents the variation of impedance $(Z)$ of a series $LCR$ circuit with the frequency $(v)$ of the applied $a.c.$?