In the given $AC$ circuit,when switch $S$ is at position $1$,the source $emf$ leads the current by $\pi / 6$. Now,if the switch is at position $2$,then

Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $e.m.f$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.

$A$ series $LR$ circuit is connected to a voltage source with $V(t) = V_0 \sin \omega t$. After a very large time,how does the current $I(t)$ behave? (Given: $t_0 \gg \frac{L}{R}$)

An $LCR$ series circuit with $100 \,\Omega$ resistance is connected to an $AC$ source of $200 \,V$ and angular frequency $300 \,rad/s$. When only the capacitance is removed,the current leads the voltage by $60^o$. When only the inductance is removed,the current lags the voltage by $60^o$. Then the current and power dissipated in the $LCR$ circuit are respectively:

$L$,$C$,and $R$ denote inductance,capacitance,and resistance respectively. Pick out the combination which does not have the dimensions of frequency.

If $C, R, L$ and $I$ denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are :
$(1)$ $C R$
$(2)$ $\frac{L}{R}$
$(3)$ $\sqrt{L C}$
$(4)$ $L I^2$