The adjoining figure shows an $AC$ circuit with resistance $R$,inductance $L$ and source voltage $V_s$. Then

$A$ radio can tune over the frequency range of a portion of $MW$ broadcast band: ($800 \;kHz$ to $1200 \;kHz$). If its $LC$ circuit has an effective inductance of $200 \;\mu H$,what must be the range of its variable capacitor?

$A$ $100 \;\mu F$ capacitor in series with a $40 \;\Omega$ resistance is connected to a $110 \;V, 12 \;kHz$ supply.
$(a)$ What is the maximum current in the circuit?
$(b)$ What is the time lag between the current maximum and the voltage maximum?
Hence,explain the statement that a capacitor is a conductor at very high frequencies. Compare this behaviour with that of a capacitor in a $dc$ circuit after the steady state.

In an $LCR$ series circuit,an inductor $30 \, {mH}$ and a resistor $1 \, \Omega$ are connected to an $AC$ source of angular frequency $300 \, {rad/s}$. The value of capacitance for which the current leads the voltage by $45^{\circ}$ is $\frac{1}{x} \times 10^{-3} \, {F}$. Then the value of $x$ is ..... .

$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.
$(a)$ What is the maximum current in the coil?
$(b)$ What is the time lag between the voltage maximum and the current maximum?

$A$ resistance of $200 \ \Omega$ and an inductor of $\frac{1}{2 \pi} \ H$ are connected in series to an a.c. voltage of $40 \ V$ and $100 \ Hz$ frequency. The phase angle between the voltage and current is