$A$ $L-C-R$ series $AC$ circuit is tuned to resonance. The impedance of the circuit is now . . . . . . .

In a series $L-C-R$ circuit,the capacitance is changed from $C$ to $2C$. To obtain the same resonance frequency,the inductance should be changed from $L$ to:

At which point is the circuit inductive?

In a series $LCR$ circuit,resonance occurs at frequency $f = f_0$. If at this moment the amplitude of current is $I_0$,then calculate the wattless current at the same moment.

$A$ series $LCR$ circuit with $L=0.12\, H$,$C=480\, nF$,$R=23\, \Omega$ is connected to a $230\, V$ variable frequency supply.
$(a)$ What is the source frequency for which current amplitude is maximum? Obtain this maximum value.
$(b)$ What is the source frequency for which average power absorbed by the circuit is maximum? Obtain the value of this maximum power.
$(c)$ For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
$(d)$ What is the $Q$-factor of the given circuit?

$A$ 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 $\text{ kHz}$)