The graph shows the variation of current $I$ with frequency $f$ for a series $R-L-C$ network. Keeping $L$ and $C$ constant,if resistance $R$ decreases:

$A$ 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 $\text{ kHz}$)

$A$ circuit of negligible resistance has an inductor of $0.16 H$ and a capacitor of $25 \mu F$ connected in series with an alternating voltage source. The resonant frequency of the circuit is:

In the circuit shown in the figure, the voltmeter reads $75 \, V$. The value of $C$ is ....... $\mu F$.

$A$ series $LCR$ circuit containing $5.0 \, H$ inductor,$80 \, \mu F$ capacitor,and $40 \, \Omega$ resistor is connected to a $230 \, V$ variable frequency $AC$ source. The angular frequencies of the source at which the power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

For a series $LCR$ circuit,the $I$ vs $\omega$ curve is shown. Consider the following statements:
$(A)$ To the left of $\omega_{r}$,the circuit is mainly capacitive.
$(B)$ To the left of $\omega_{r}$,the circuit is mainly inductive.
$(C)$ At $\omega_{r}$,the impedance of the circuit is equal to the resistance of the circuit.
$(D)$ At $\omega_{r}$,the impedance of the circuit is $0$.
Choose the most appropriate answer from the options given below: