$A$ resistor of resistance $40 \Omega$,a capacitor of capacitive reactance $20 \Omega$,and an inductor of inductive reactance $50 \Omega$ are connected in series to an $ac$ source of $100 \ V$. The current through the circuit is (in $A$)

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 $LR$ circuit,$X_L = 3R$. Now,a capacitor with $X_C = R$ is added in series. What is the ratio of the new power factor to the old power factor?

The figure shows a combination of inductances and capacitances. The resonant frequency of the $L-C$ circuit is:

$A$ circuit containing an $80 \; mH$ inductor,a resistance of $15 \; \Omega$,and a $60 \; \mu F$ capacitor in series is connected to a $230 \; V, 50 \; Hz$ supply. Obtain the average power transferred to each element of the circuit,and the total power absorbed.

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 $\,V$)