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 an electrical circuit,$R, L, C$ and an $AC$ voltage source are all connected in series. When $L$ is removed from the circuit,the phase difference between the voltage and the current in the circuit is $\pi / 3$. If instead,$C$ is removed from the circuit,the phase difference is again $\pi / 3$. The power factor of the circuit is

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 $R-L-C$ 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.....$W$

For a series $LCR$ circuit,which of the following statements is correct?

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