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

In an $LCR$ circuit, the resonant frequency is $600 \ Hz$ and the half-power points are at $650 \ Hz$ and $550 \ Hz$. The quality factor is:

An alternating current is flowing through a series $L-C-R$ circuit. It is found that the current reaches a value of $1 \ mA$ at both $200 \ Hz$ and $800 \ Hz$ frequency. What is the resonance frequency of the circuit (in $Hz$)?

In a series $LCR$ circuit,a resistor of $300 \ \Omega$,a capacitor of $25 \ \text{nF}$ and an inductor of $100 \ \text{mH}$ are used. For maximum current in the circuit,the angular frequency of the ac source is $. . . . \times 10^4 \ \text{rad s}^{-1}$.

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:

What is the value of inductance $L$ in $mH$ for which the current is maximum in a series $LCR$ circuit with $C = 10 \, \mu F$ and $\omega = 1000 \, rad/sec$?