Reactance and impedance

A series LR circuit is connected to a voltage source with $V(t)=V_0\sin\Omega t$. After very large time, current I(t) behaves as $\left(t_0>>\dfrac LR\right)$ :

When the rms voltages $V_L$, $V_C$ and $V_R$ are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio $V_L:V_C:V_R=1:2:3$. If the rms voltage of the AC source is 100 V, then $V_R$ is close to :

A sinusoidal voltage $V(t)=100\sin(500t)$ is applied across a pure inductance of $L=0.02$ H. The current through the coil is :

In the given circuit, the AC source has $\omega=100$ rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current $I_R$ through the resistor and voltage $V_C$ across the capacitor are compared in the two cases. Which of the following is/are true?

A series R-C combination is connected to an AC voltage of angular frequency $\omega=500$ radian/s. If the impedance of the R-C circuit is $R\sqrt{1.25}$, the time constant (in millisecond) of the circuit is

An AC voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $\omega$ is increased

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current $I$ (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column I. Match the two.