A $100 \;\mu \,F$ capacitor in series with a $40\; \Omega$ resistance is connected to a $110\; V , 12\; k\,Hz$ 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.

One $10\, \,\,V, 60\, W$ bulb is to be connected to $100\, V$ line. The required induction coil has self inductance of value $(f = 50\,Hz)$

$AC$ alternating emf $\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$ volt is applied to a capacitor of $2 \mu \mathrm{F}$, the rms value of current in the circuit is.. . . . . .$\mathrm{mA}$.

In an $ac$ circuit, the potential difference across an inductance and resistance joined in series are respectively $16\, V$ and $20 \,V$. The total potential difference across the circuit is…….$V$

Frequency of $L-C$ circuit is $f_{1} .$ If a resistance $R$ is also added to
it, the frequency becomes $f_{2}$. The ratio of $\frac{f_{2}}{f_{1}}$ will be