$L, C, R$ represent physical quantities inductance,capacitance,and resistance respectively. The combinations which have the dimensions of frequency are

$A$ series $LCR$ circuit is connected across a source of alternating emf of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance is increased $(R)$ by $1.4$ times,the resonant frequency now is

An $L-C-R$ circuit is connected to a source of $A.C.$ current. At resonance,the phase difference between the applied voltage and the current in the circuit is:

In a series $LCR$ circuit,$C = 2 \mu F$,$L = 1 \text{ mH}$,and $R = 10 \Omega$. The ratio of the energies stored in the inductor and the capacitor,when the maximum current flows in the circuit,is:

$A$ series $LCR$ circuit is connected to a $45 \sin (\omega t) \text{ V}$ source. The resonant angular frequency of the circuit is $10^5 \text{ rad s}^{-1}$ and current amplitude at resonance is $I_0$. When the angular frequency of the source is $\omega = 8 \times 10^4 \text{ rad s}^{-1}$, the current amplitude in the circuit is $0.05 I_0$. If $L = 50 \text{ mH}$, match each entry in List-$I$ with an appropriate value from List-$II$ and choose the correct option.

List-$I$	List-$II$
$(P)$ $I_0$ in $\text{mA}$	$(1)$ $44.4$
$(Q)$ The quality factor of the circuit	$(2)$ $18$
$(R)$ The bandwidth of the circuit in $\text{rad s}^{-1}$	$(3)$ $400$
$(S)$ The peak power dissipated at resonance in $\text{Watt}$	$(4)$ $2250$
	$(5)$ $500$

An inductor of $0.5 \,mH$,a capacitor of $200 \,\mu F$ and a resistor of $2 \,\Omega$ are connected in series with a $220 \,V$ ac source. If the current is in phase with the emf,the frequency of ac source will be ................ $\times 10^{2} \,Hz$