$A$ 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 $mH$)

In a series $LCR$ circuit, the voltage across $R$ is $100 \text{ V}$, $R = 1 \text{ k}\Omega$ and $C = 2 \mu\text{F}$. The angular frequency $\omega$ is $200 \text{ rad s}^{-1}$. At resonance, the voltage across '$L$' is (in $V$)

An $L-C-R$ series circuit with $100 \, \Omega$ resistance is connected to an $ac$ source of $100 \, V$ and angular frequency $300 \, rad/s$. When the capacitance is removed, the current lags behind the voltage by $45^{\circ}$. When the inductance is removed, the current leads the voltage by $45^{\circ}$. The current flowing in the circuit will be ... $A$.

Obtain the resonant frequency $\omega_{r}$ of a series $LCR$ circuit with $L=2.0 \;H, C=32\; \mu F$ and $R=10\; \Omega$. What is the $Q$-value of this circuit?

$A$ tuned amplifier circuit is used to generate a carrier frequency of $ 2 \text{ MHz} $ for amplitude modulation. The value of $ \sqrt{LC} $ is

When the frequency of the $AC$ voltage applied to a series $LCR$ circuit is gradually increased from a low value, the impedance of the circuit