An electric lamp connected in series with a capacitor and an $A.C.$ source is glowing with a certain brightness. On increasing the value of capacitance,the brightness of the lamp

$A$ $100 \;\mu F$ 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.

$A$ 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?

Which of the following dimensions will be the same as that of time?

An electric lamp connected in series with a capacitor and an a.c. source is glowing with certain brightness. On reducing the frequency of the source, the brightness of the lamp

An alternating voltage is connected in series with a resistance $R$ and an inductance $L$. If the potential drop across the resistance is $200 \, V$ and across the inductance is $150 \, V$,then the applied voltage is.......$V$.