The power factor of an $LCR$ circuit at resonance is:

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 :

$A$ resonant frequency of a circuit is $f$. If the capacitance is made four times the initial value,then the resonant frequency will become

The readings of the ammeter and voltmeter in the following circuit are respectively:

In an a.c. $LCR$ circuit,a capacitor and an inductor in series are connected with an a.c. voltage source of $90\,V$. An ammeter and a voltmeter are connected in the circuit to measure the current in the circuit and the voltage across the capacitor plus the inductor combination. If $X_L = X_C = 4\,\Omega$ and $R = 45\,\Omega$,the readings of the ammeter $(I)$ and the voltmeter $(V)$ are:

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