In the circuit shown,the $AC$ source has voltage $V=20 \cos (\omega t) \text{ V}$ with $\omega=2000 \text{ rad/s}$. The magnitude of the amplitude current will be nearly

$A$ telephone wire of length $200\, km$ has a capacitance of $0.014\, \mu F$ per km. If it carries an $AC$ of frequency $5\, kHz$,what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum? (in $mH$)

Using a variable-frequency a.c. voltage source, the maximum current measured in the given $LCR$ circuit is $50 \text{ mA}$ for $V = 5 \sin(100t)$. The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor $(C)$ used is . . . . . . $\mu\text{F}$.

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

In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad/s$. At resonance,the voltage across $L$ is......$V$.

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?