In a series $LCR$ circuit, the voltage across $R$ is $100 \text{ V}$, $R = 1 \text{ k}\Omega$ and $C = 2 \mu\text{F}$. The angular frequency $\omega$ is $200 \text{ rad s}^{-1}$. At resonance, the voltage across '$L$' is (in $V$)

For a given series $LCR$ circuit,it is found that maximum current is drawn when the value of the variable capacitance is $2.5 \ nF$. If a resistance of $200 \ \Omega$ and a $100 \ mH$ inductor are being used in the given circuit,the frequency of the $AC$ source is $... \times 10^3 \ Hz$. (Given $\pi^2 = 10$)

An $ac$ source of variable frequency $f$ is connected to an $LCR$ series circuit. Which one of the graphs represents the variation of current $I$ in the circuit with frequency $f$?

In a radio tuning $RLC$ circuit,the half-power frequencies are $100 \, MHz$ and $120 \, MHz$. Find the quality factor.

In the circuit shown,the ratio of the quality factor to the bandwidth is: (in $\text{ s}$)

Given below are two statements:
Statement $I$: Maximum power is dissipated in a circuit containing an inductor, a capacitor, and a resistor connected in series with an $AC$ source, when resonance occurs.
Statement $II$: Maximum power is dissipated in a circuit containing a pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct answer from the options given below: