An $R-L-C$ circuit consists of a $150 \Omega$ resistor,$20 \mu F$ capacitor,and a $500 mH$ inductor connected in series with a $100 V$ $AC$ supply. The angular frequency of the supply voltage is $400 rad s^{-1}$. The phase angle between the current and the applied voltage is

In an a.c. circuit containing $L, C$ and $R$ in series,the ratio of apparent power to the true power is ($Z$ and $R$ are the impedance and resistance respectively,$\phi$ = phase angle).

Study the circuits $(a)$ and $(b)$ shown in the figure and answer the following questions.
$(a)$ Under which conditions would the $rms$ currents in the two circuits be the same?
$(b)$ Can the $rms$ current in circuit $(b)$ be larger than that 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

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 $a.c.$?

In a series $LCR$ circuit,the resistance is $18 \ \Omega$ and the impedance is $33 \ \Omega$. An $r.m.s.$ voltage of $220 \ V$ is applied across the circuit. The true power consumed in the $a.c.$ circuit is: (in $W$)