In an $LCR$ circuit,the resonating frequency is $500 \,kHz$. If the value of $L$ is doubled and the value of $C$ is decreased to $\frac{1}{8}$ times its initial value,then the new resonating frequency in $kHz$ will be .......

In a series $LCR$ circuit, $C = 2 \mu F$, $L = 5 \text{ mH}$, and $R = 5 \Omega$. What is the ratio of the energy stored in the inductor to that in the capacitor when the maximum current flows through the circuit (in $:$)?

An alternating $e.m.f.$ of frequency $v = \frac{1}{2\pi \sqrt{LC}}$ is applied to a series $LCR$ circuit. For this frequency of the applied $e.m.f.$:

For a series $LCR$ circuit,the power loss at resonance is

An inductor of inductance $2 \mu H$ is connected in series with a resistance,a variable capacitor and an a.c. source of frequency $5 \text{ kHz}$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x} \text{ F}$,where the value of '$x$' is (Take $\pi^2 = 10$).

Obtain an equation for the sharpness of resonance in an $L-C-R$ series $AC$ circuit. What is the quality factor $Q$? Explain bandwidth.