$A$ lamp consumes only $50 \%$ of maximum power in an $AC$ circuit. What is the phase difference between the applied voltage and the circuit current?

If the power factor changes from $0.5$ to $0.25$ because impedance changes from $Z_1$ to $Z_2$, then $Z_1 = x Z_2$. The value of $x$ is (Resistance remains constant).

What is power factor and voltage-current relationship in an $AC$ circuit?

In an $A.C.$ circuit containing $L, C, R$ in series,the ratio of true power to apparent power is ($Z=$ impedance of the circuit and $R$ is the resistance).

In a series $LCR$ circuit,$R = 18 \ \Omega$ and the impedance $Z = 30 \ \Omega$. An $rms$ voltage of $210 \ V$ is applied across the circuit. The true power consumed in the $AC$ circuit is nearly: (in $W$)

$A$ capacitor $C = 2 \mu F$ and an inductor with $L = 10 H$ and coil resistance $R = 5 \Omega$ are connected in series in a circuit. When an alternating current of $r.m.s.$ value $I_{rms} = 2 A$ flows in the circuit,the average power in watts in the circuit is: