In an $LCR$ circuit,$R = 100 \ \Omega$. When the capacitor $C$ is removed,the current lags behind the voltage by a phase of $\pi / 3$. When the inductor $L$ is removed,the current leads the voltage by a phase of $\pi / 3$. What is the impedance of the circuit in $\Omega$?

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 .......... $\Omega$.

In an $LCR$ series circuit, if the potential differences across the inductor, capacitor, and resistor are $60 \,V$, $30 \,V$, and $40 \,V$ respectively, then the $AC$ voltage applied to the circuit is: (in $\,V$)

An inductor $20 \, mH$,a capacitor $50 \, \mu F$ and a resistor $40 \, \Omega$ are connected in series across a source of emf $V = 10 \, \sin \, 340t$. The power loss in the $A.C.$ circuit is ...... $W$.

In the given circuit,the peak voltages across $C$,$L$,and $R$ are $30 \,V$,$110 \,V$,and $60 \,V$,respectively. The rms value of the applied voltage is (in $\,V$)

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: