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 an $AC$ circuit,$V$ and $I$ are given below. Find the power dissipated in the circuit:
$V = 50 \sin(50t) \ V$
$I = 50 \sin(50t + \frac{\pi}{3}) \ mA$ (in $W$)

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 an $A.C.$ circuit containing $L, C, R$ in series,the ratio of true power to apparent power is ($Z=$ impedance of the circuit and $R$ is the resistance).

An inductor $20 \, mH$,a capacitor $100 \, \mu F$ and a resistor $50 \, \Omega$ are connected in series across a source of emf,$V = 10 \sin(314 \, t)$. The power loss in the circuit is ...... $W$.

$A$ 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