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).

In an $AC$ circuit $E = 200 \sin(50t) \text{ V}$ and $I = 100 \sin(50t + \frac{\pi}{3}) \text{ mA}$. The power dissipated in the circuit is (Given: $\sin 30^{\circ} = \cos 60^{\circ} = 0.5$,$\sin 60^{\circ} = \cos 30^{\circ} = \frac{\sqrt{3}}{2}$) (in $watt$)

The average power dissipated in an $A.C.$ circuit is $2 \ W$. If the current flowing through the circuit is $2 \ A$ and the impedance is $1 \ \Omega$,what is the power factor of the $A.C.$ circuit?

$A$ series $LCR$ circuit is connected to an $AC$ source of voltage $V = 150 \sin(80 \pi t) \text{ V}$. If the resistance of the resistor in the circuit is $25 \ \Omega$ and the impedance in the circuit is $75 \ \Omega$, the average power dissipated per cycle in the circuit is: (in $\text{ W}$)

$A$ circuit,consisting of an inductance and a resistance in series,is connected to a $250 \ V$ $A$.$C$. supply. It draws a current of $10 \ A$. If the power consumed in the circuit is $1500 \ W$,calculate the wattless current. (in $A$)

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 $W$.