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).

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).

$A$ choke coil is connected to an $AC$ source of frequency $\frac{50}{\pi} \, Hz$. If the resistance of the coil is $1 \, \Omega$ and the inductance is $10 \, mH$,what would be the value of the power factor?

$A$ $LCR$ series circuit driven with $V_{rms} = 90 \text{ V}$ at frequency $f_d = 30 \text{ Hz}$ has resistance $R = 80 \text{ }\Omega$,an inductance with inductive reactance $X_L = 20.0 \text{ }\Omega$ and capacitance with capacitive reactance $X_C = 80.0 \text{ }\Omega$. The power factor of the circuit is . . . . . . .

$A$ series $LCR$ circuit is connected to an $AC$ source of voltage $V = 150 \sin(80 \pi t) \text{ V}$. If the resistance of the resistor in the circuit is $25 \ \Omega$ and the impedance in the circuit is $75 \ \Omega$, the average power dissipated per cycle in the circuit is: (in $\text{ W}$)

The power factor of the circuit shown in the figure is: