The reactance of a capacitor of capacitance $C \mu F$ for an $ac$ frequency of $\frac{400}{\pi} \ Hz$ is $25 \ \Omega$. The value of $C$ is ..... $\mu F$.

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 value of the current through an inductance of $1 \, H$ and of negligible resistance,when connected to an $ac$ source of $200 \, V$ and $50 \, Hz$ is: (in $, A$)

An alternating voltage $V = 300\sqrt{2} \sin(100t)$ is connected to a $1 \ \mu F$ capacitor through an $AC$ ammeter. The reading of the ammeter will be.....$mA$.

$A$ device $'X'$ is connected to an a.c. source. The variation of voltage,current,and power in one complete cycle is shown in the figure.
$(a)$ Which curve shows power consumption over a full cycle?
$(b)$ What is the average power consumption over a cycle?
$(c)$ Identify the device $'X'$.

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 $I = I_m \sin(\omega t)$):