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 $. . . . \times 10^4 \ \text{rad s}^{-1}$.

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:

$A$ series $LCR$ circuit with $R=20\; \Omega, L=1.5\; H$ and $C=35\; \mu F$ is connected to a variable-frequency $200\; V$ $ac$ supply. When the frequency of the supply equals the natural frequency of the circuit,what is the average power (in $W$) transferred to the circuit in one complete cycle?

An $LC$ circuit consists of a capacitor and a coil with a large number of turns. Suppose all the linear dimensions of all elements of the circuit are increased by a factor of $2$ while keeping the number of turns on the coil constant. How much does the resonant frequency of the circuit change?

The quality factor of an $LCR$ circuit having resistance $(R)$ and inductance $(L)$ at resonance frequency $(\omega)$ is given by:

$A$ resistor $R$,an inductor $L$,and a capacitor $C$ are connected in series to an oscillator of frequency $n$. If the resonant frequency is $n_r$,then the current lags behind the voltage when: