$A$ 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 . . . . . . .

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).

The power factor of an $ac$ circuit having resistance $(R)$ and inductance $(L)$ connected in series and an angular velocity $\omega$ is:

In an $AC$ circuit,$I = 5 \sin \left( 100t - \frac{\pi}{2} \right)$ and $V = 200 \sin 100t$. The power consumed is

An inductor and a resistor of $25 \Omega$ are connected in series to an ac source of voltage $100 \sin (100 \pi t) \ V$. If the impedance of the circuit is $50 \Omega$,the average power dissipated per cycle in the circuit is: (in $W$)