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

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 $W$)

In an $a.c.$ circuit,voltage and current are given by: $V=100 \sin (100 t) \ V$ and $I=100 \sin (100 t + \frac{\pi}{3}) \ mA$ respectively. The average power dissipated in one cycle is: (in $W$)

In an $AC$ circuit,the instantaneous values of emf and current are $e = 200 \sin(314t) \text{ V}$ and $I = \sin(314t + \frac{\pi}{3}) \text{ A}$. The average power consumed in watt is

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

An e.m.f. $e=E_0 \cos \omega t$ is applied to a circuit containing $L, C$ and $R$ in series where $X_L=3 R$ and $X_C=R$. The average power dissipated in the circuit is