At a particular angular frequency,the reactance of a capacitor and that of an inductor are the same. If the angular frequency is doubled,the ratio of the reactance of the capacitor to that of the inductor will be:

An $AC$ source of $20\,V$ (assuming standard frequency $f = 50\,Hz$ for calculation) is connected to an inductance of $100\,mH$,a capacitance of $100\,\mu F$,and a resistance of $120\,\Omega$ as shown in the figure. The time in which the resistance,having a thermal capacity of $2\,J/^{\circ}C$,will get heated by $16^{\circ}C$ is ..........$s$.

$A$ bulb is connected first with $DC$ and then $AC$ of the same voltage. In which case will it shine more brightly?

An initially charged undriven $LCR$ circuit having inductance $L$,capacitance $C$ and resistance $R$ will be:

The figure shows a system of an inductor and a parallel plate capacitor made of $2$ parallel circular plates of area $A$,filled with a dielectric liquid of dielectric constant $K$. $A$ small leak develops in the capacitor,and the liquid starts to fill the inductor of the same dimensions having $n$ turns per unit length. Find the ratio of the magnitude of the initial reactance to the final reactance of the circuit after the liquid fills the inductor completely.
Given: $\omega^2 A^2 n^2 = c^2$
$\omega \rightarrow$ angular frequency of $AC$
$c \rightarrow$ speed of light
$\mu_r \rightarrow$ relative permeability of the liquid

$A$ resistor of resistance $R$ and an inductor of inductive reactance $R$ are connected in series to an $AC$ source. $A$ capacitor of capacitive reactance $2R$ is then connected in series with $L$ and $R$. The ratio of the power factors of the $LR$ and $LCR$ circuits is: