What is the average power dissipation in an ideal capacitor in an $AC$ circuit?

The reactance of a capacitor at $50 \ Hz$ is $5 \ \Omega$. If the frequency is increased to $100 \ Hz$,the new reactance is (in $\Omega$)

The reactance of a capacitor is $X_{C}$. If the frequency and the capacitance are doubled,then the new reactance will be

Discuss power in an $AC$ circuit containing only a capacitor.

In a capacitive circuit,the reactance of a capacitor at frequency $f$ is $X_{C}$. What will be its reactance at frequency $4f$?

Let $f = 50\, Hz$ and $C = 100\, \mu F$ in an $AC$ circuit containing a capacitor only. If the peak value of the current in the circuit is $1.57\, A$,the expression for the instantaneous voltage across the capacitor will be (assuming current is $I = I_m \sin(\omega t)$):