An oscillating circuit consists of a capacitor with capacitance $C = 10 \, \mu F$, a coil with inductance $L = 6.0 \, \mu H$, and active resistance $R = 10 \, \Omega$. The mean power that should be fed to the circuit to maintain undamped harmonic oscillations with an external driving source of frequency $f = 50 \, Hz$ and peak voltage $V_m = 280 \, V$ is:

$A$ 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.....$W$

An inductor of inductance $L$,a capacitor of capacitance $C$,and a resistor of resistance $R$ are connected in series to an $AC$ source of potential difference $V$ volts as shown in the figure. The potential difference across $L$,$C$,and $R$ is $40 \, V$,$10 \, V$,and $40 \, V$,respectively. The amplitude of the current flowing through the $LCR$ series circuit is $10 \sqrt{2} \, A$. The impedance of the circuit is .......... $\Omega$.

Draw phasor diagrams for $X_C > X_L$ and $X_C < X_L$,and state the disadvantages of the phasor method.

When $L$, $C$, and $R$ are connected in series with an $AC$ source of frequency $f$, the current leads the voltage by a phase angle of $45^{\circ}$. What is the value of $C$?

In the given circuit,the $AC$ source has $\omega = 100 \ rad/s$. Considering the inductor and capacitor to be ideal,the correct choice$(s)$ is(are):
$(A)$ The current through the circuit,$I$ is $0.3 \ A$
$(B)$ The current through the circuit,$I$ is $0.3 \sqrt{2} \ A$
$(C)$ The voltage across $100 \ \Omega$ resistor $= 10 \sqrt{2} \ V$
$(D)$ The voltage across $50 \ \Omega$ resistor $= 10 \sqrt{2} \ V$