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:

In a series $LCR$ resonant circuit,the quality factor is measured as $100$. If the inductance is increased by two fold and resistance is decreased by two fold,then the quality factor after this change will be .........

$A$ resistor of $100 \Omega$,an inductor of self-inductance $(\frac{4}{\pi^2}) \text{ H}$,and a capacitor of unknown capacitance are connected in series to an $A$.$C$. source of $200 \text{ V}, 50 \text{ Hz}$. When the current and voltage are in phase,the capacitance and the power dissipated are respectively:

For a series $LCR$ circuit at resonance,the statement which is not true is:

$A$ transmitting station releases waves of wavelength $960\, m$. $A$ capacitor of $2.56\, \mu F$ is used in the resonant circuit. The self-inductance of the coil necessary for resonance is $............ \times 10^{-8}\, H$.

For the series $LCR$ circuit shown in the figure,what is the resonance frequency and the amplitude of the current at the resonating frequency?