In an $A.C.$ circuit,the instantaneous values of $\text{e.m.f}.$ and current are $e = 10 \sin(50 \pi t) \text{ V}$ and $I = 10 \sin(50 \pi t + \frac{\pi}{3}) \text{ A}$. The average power consumed in the circuit is $... \text{ W}$.

The impedance of a circuit consists of $3 \, \Omega$ resistance and $4 \, \Omega$ reactance. The power factor of the circuit is

In the circuit shown in the figure,if the value of $rms$ current is $2.2\, A$,the power factor of the box is:

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 $W$)

The power dissipated in a resistor of resistance $R$ when an alternating current with a peak value of $I_p$ flows through it is:

$A$ $LCR$ 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 . . . . . . .