In an $LCR$ series circuit $R=10 \,\Omega, X_L=8 \,\Omega$ and $X_C=6 \,\Omega$. The total impedance of the circuit is ........ $\Omega$.

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

$A$ capacitance of $\left(\frac{10^{-3}}{2 \pi}\right) F$,an inductance of $\left(\frac{100}{\pi}\right) mH$,and a resistance of $10 \Omega$ are connected in series with an $AC$ voltage source of $220 V, 50 Hz$. The phase angle of the circuit is (in $^{\circ}$)

$A$ rejector circuit is the resonant circuit in which

The power factor of an $L-R$ series circuit is $0.6$ and that of a $C-R$ series circuit is $0.5$. If the elements ($L, C,$ and $R$) of the two circuits are joined in series,the power factor of this circuit is found to be $1$. The ratio of the resistance in the $L-R$ circuit to the resistance in the $C-R$ circuit is:

In a series $L-C-R$ circuit,the inductive reactance is twice the resistance and the capacitive reactance is $1/3$ rd of the inductive reactance. The power factor of the circuit is