Capacitive reactance of a capacitor in an $AC$ circuit is $3 \ k\Omega$. If this capacitor is connected to a new $AC$ source of double frequency,the capacitive reactance will become:

$A$ capacitor '$C$' is connected across a $DC$ source,the reactance of the capacitance will be . . . . . . .

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

The reactance of a coil when used in the domestic $ac$ power supply $(220\, V, 50\, Hz)$ is $100\, \Omega$. The self-inductance of the coil is nearly........$H$.

An alternating $emf$ $E = 440 \sin(100 \pi t)$ is applied to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi} \text{ H}$. If an $AC$ ammeter is connected in the circuit,its reading will be $....... \text{ A}$.

The frequency for which a $5 \mu F$ capacitor has a reactance of $\frac{1}{1000} \Omega$ is given by