For an $AC$ circuit,the potential difference and current are given by $V = 10 \sqrt{2} \sin \omega t$ (in $V$) and $I = 2 \sqrt{2} \cos \omega t$ (in $A$) respectively. The power dissipated in the instrument is ............ $W$.

In a series $LCR$ circuit,the inductive reactance $(X_{L})$ is $10\, \Omega$ and the capacitive reactance $(X_{C})$ is $4\, \Omega$. The resistance $(R)$ in the circuit is $6\, \Omega$. The power factor of the circuit is :

The $r.m.s.$ current in an $ac$ circuit is $2 \ A$. If the wattless current is $\sqrt{3} \ A$,the power factor is:

In an $AC$ circuit,the voltage and current are described by $V = 200 \sin(314t - \frac{\pi}{6}) \text{ V}$ and $i = 50 \sin(314t + \frac{\pi}{6}) \text{ mA}$ respectively. The average power dissipated in the circuit is $...... \text{ W}$.

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

Two electric circuits $A$ and $B$ are shown in the figure. The ratio of power factor of circuit $B$ to that of circuit $A$ is