Power consumed in an $AC$ circuit becomes zero if

The potential difference $V$ and the current $I$ flowing through an instrument in an $AC$ circuit of frequency $f$ are given by $V = 5 \cos(\omega t)$ volts and $I = 2 \sin(\omega t)$ amperes (where $\omega = 2 \pi f$). The power dissipated in the instrument is......$W$

In a series $LCR$ circuit, the alternating e.m.f. and current are given by the equations $V = V_0 \sin(\omega t)$ and $I = I_0 \sin(\omega t + \frac{\pi}{3})$ respectively. The average power dissipated in the circuit over one cycle of a.c. is $(\cos 60^{\circ} = 0.5)$.

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 $...... \text{ W}$.

$A$ series $LCR$ circuit is connected to an a.c. source of $230 \ V, 50 \ Hz$. The circuit contains a resistance of $80 \ \Omega$,an inductor having inductive reactance $70 \ \Omega$,and a capacitor of capacitive reactance $130 \ \Omega$. The power factor of the circuit is $x$. The value of $x$ is