In an $A.C.$ circuit,the current flowing in an inductance is $I = 5\,\sin\,(100\,t - \pi/2)\,A$ and the potential difference is $V = 200\,\sin\,(100\,t)\,V$. The power consumption is equal to......$W$.

$A$ group of electric lamps having a total power rating of $1000 \text{ W}$ is supplied by an $AC$ voltage $E = 200 \sin(310t + 60^\circ)$. Then the $rms$ value of the circuit current is

In a series $LCR$ circuit,$R = 18 \ \Omega$ and the impedance $Z = 33 \ \Omega$. An $RMS$ voltage of $220 \ V$ is applied across the circuit. The true power consumed in the $AC$ circuit is: (in $W$)

In an $A.C.$ circuit,the instantaneous values of $\text{e.m.f}.$ and current are $e = 10 \sin(50 \pi t) \text{ V}$ and $I = 10 \sin(50 \pi t + \frac{\pi}{3}) \text{ A}$. The average power consumed in the circuit is $... \text{ W}$.

In an $AC$ circuit,$V$ and $I$ are given by $V = 150 \sin(150t) \, V$ and $I = 150 \sin(150t + \frac{\pi}{3}) \, A$. The power dissipated in the circuit 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 :