The power in an $AC$ circuit is given by $P = E_{rms}I_{rms} \cos \phi$. The value of $\cos \phi$ in a series $LCR$ circuit at resonance is:

The output voltage (taken across the resistance) of an $L-C-R$ series resonant circuit falls to half its peak value at a frequency of $200 \,Hz$ and again reaches the same value at $800 \,Hz$. The bandwidth of this circuit is ............. $\,Hz$.

In a series $LCR$ circuit,the voltage leads the current when (Given that $\omega_0$ is the resonant angular frequency):

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 $L-C-R$ circuit containing a resistance $R$ has angular frequency $\omega$. At resonance,the voltages across the resistance and the inductor are $V_R$ and $V_L$ respectively. The value of the capacitance is:

$A$ series $LCR$ circuit containing a resistance of $120\,\Omega$ has a resonance frequency of $4 \times 10^5\, rad\, s^{-1}$. The voltages,at resonance,across the resistance and inductance are $60\,V$ and $40\,V$ respectively. The values of $L$ and $C$ respectively are: