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

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 instantaneous values of current and potential difference in an alternating circuit are $i = \sin \omega t$ and $E = 100 \cos \omega t$ respectively. The $r.m.s.$ value of the wattless current (in $A$) in the circuit is:

In an $ac$ circuit,the current is given by $i = 5 \sin \left( 100 t - \frac{\pi}{2} \right)$ and the $ac$ potential is $V = 200 \sin (100 t) \text{ volts}$. Then the power consumption is $....... \text{ watts}$.

In an $AC$ circuit $E = 50 \sin(500t)$ $V$, $I = 600 \sin(500t + \frac{\pi}{3})$ mA. What is the power dissipated in the circuit (in $\text{ W}$)? [$\cos 60^{\circ} = 0.5$]

$(a)$ For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.
$(b)$ Power factor can often be improved by the use of a capacitor of appropriate capacitance in the circuit. Explain.