When an AC source is connected to an ideal capacitor

A lamp is connected in series with a capacitor. Predict your observations when the system is connected first across a DC and then an AC source. What happens in each case, if the capacitance of the capacitor is reduced?

When DC source is connected, the condenser is charged but no current flows in the circuit. Therefore, the lamp does not glow. No change occurs even when capacitance of capacitor is reduced.
When AC source is connected, the capacitor offers
capacitive reactance Xc =1/ ωc The current flows in the circuit and the lamp glows. On reducing C, Xc increases. Therefore, glow of the bulb reduces.