$A$ $15.0 \mu\text{F}$ capacitor is connected to a $220 \text{ V}$, $50 \text{ Hz}$ source. The capacitive reactance of the circuit is . . . . . . $\Omega$.

Explain the representation of $AC$ current and voltage by rotating vectors.

An alternating voltage $V(t) = 220 \sin(100 \pi t)$ volt is applied to a purely resistive load of $50 \ \Omega$. The time taken for the current to rise from half of the peak value to the peak value is: (in $ms$)

An alternating voltage $E = 200 \sqrt{2} \sin(100 t) \text{ V}$ is connected to a $1 \mu\text{F}$ capacitor through an $A.C.$ ammeter. The reading of the ammeter shall be: (in $\text{ mA}$)

An $AC$ voltage of $10 \sin \omega t$ volt is applied to a pure inductor of inductance $10 \ H$. The current through the inductor in ampere is

The average power dissipation in a pure capacitance in an $AC$ circuit is