$A$ resistor of $100 \Omega$, an inductor of $\frac{25}{\pi^2} \text{ mH}$ and a capacitor of $0.1 \mu\text{F}$ are connected in series to an $AC$ source. The impedance of the circuit is minimum for a frequency of (in $\text{ kHz}$)

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

An inductor of $0.5\,mH$,a capacitor of $20\,\mu F$ and a resistance of $20\,\Omega$ are connected in series with a $220\,V$ $AC$ source. If the current is in phase with the $EMF$,the amplitude of the current in the circuit is $\sqrt{x}\,A$. The value of $x$ is:

In an $LC$ parallel resonance circuit,choose the wrong statement.

In an $L-C-R$ series circuit,the value of only capacitance $C$ is varied. The resulting variation of resonance frequency $f_0$ as a function of $C$ can be represented as

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 $kHz$)