$A$ capacitor of $250\,\mu F$ is connected in parallel to a coil of inductance $0.16\,mH$, while its effective resistance is $20\,\Omega$. Determine the resonant frequency.

In the circuit shown in the figure,an a.c. source gives voltage $V = 20 \cos (2000 t)$. The impedance and r.m.s. current respectively will be:

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

$A$ resistor of $100 \Omega$,an inductor of self-inductance $(\frac{4}{\pi^2}) \text{ H}$,and a capacitor of unknown capacitance are connected in series to an $A$.$C$. source of $200 \text{ V}, 50 \text{ Hz}$. When the current and voltage are in phase,the capacitance and the power dissipated are respectively:

Match List-$I$ with List-$II$ :

List-$I$	List-$II$
$(a)$ $\omega L > \frac{1}{\omega C}$	$(i)$ Current is in phase with $emf$
$(b)$ $\omega L = \frac{1}{\omega C}$	$(ii)$ Current lags behind the applied $emf$
$(c)$ $\omega L < \frac{1}{\omega C}$	$(iii)$ Maximum current occurs
$(d)$ Resonant frequency	$(iv)$ Current leads the $emf$

Choose the correct answer from the options given below :

The resonant frequency of an $L-C$ circuit is