$A$ circuit has a resistance of $12 \; \Omega$ and an impedance of $15 \; \Omega$. The power factor of the circuit will be

For an $AC$ circuit $V = 15 \sin \omega t$ and $I = 20 \cos \omega t$,the average power consumed in this circuit is ..... $W$.

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......$W$

$A$ lamp consumes only $50\%$ of peak power in an $AC$ circuit. What is the phase difference between the applied voltage and the circuit current?

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