An arc lamp requires a direct current of $10\ A$ at $80\ V$ to function. If it is connected to a $220\ V$ (rms),$50\ Hz$ $AC$ supply,the series inductor needed for it to work is close to: (in $H$)

$A$ series $R-C$ circuit is connected to an $AC$ voltage source. Consider two cases: $(A)$ when $C$ is without a dielectric medium and $(B)$ when $C$ is filled with a dielectric of constant $K = 4$. The current $I_R$ through the resistor and voltage $V_C$ across the capacitor are compared in the two cases. Which of the following is/are true?

$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a high-frequency supply $(240 \; V, 10 \; kHz)$.
$(a)$ What is the maximum current in the coil?
$(b)$ What is the time lag between the voltage maximum and the current maximum?
Hence,explain the statement that at very high frequency,an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a $DC$ circuit after the steady state?

In an $L-C-R$ circuit,the potential difference across the inductor is $60\,V$,across the capacitor is $30\,V$,and across the resistor is $40\,V$. The supply voltage will be: (in $,V$)

In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is

In an $LCR$ series circuit,the source voltage is $120 \ V$,the voltage across the inductor is $50 \ V$,and the voltage across the resistor is $40 \ V$. Determine the voltage across the capacitor.