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 ................ $\times 10^{2} \,Hz$

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

The self-inductance of the motor of an electric fan is $10\;H$. In order to impart maximum power at $50\;Hz$, it should be connected to a capacitance (in $\mu F$) of:

For a series $LCR$ circuit,the $I$ vs $\omega$ curve is shown. Consider the following statements:
$(A)$ To the left of $\omega_{r}$,the circuit is mainly capacitive.
$(B)$ To the left of $\omega_{r}$,the circuit is mainly inductive.
$(C)$ At $\omega_{r}$,the impedance of the circuit is equal to the resistance of the circuit.
$(D)$ At $\omega_{r}$,the impedance of the circuit is $0$.
Choose the most appropriate answer from the options given below:

In a series $LCR$ resonance circuit,if we change the resistance only,from a lower to higher value:

The frequency of $AC$ at which a $16 \mu F$ capacitor and a $\frac{10}{\pi^2} \ mH$ inductor will have the same reactance is: (in $kHz$)