$A$ lamp is connected in series with a capacitor. Predict your observations for $dc$ and $ac$ connections. What happens in each case if the capacitance of the capacitor is reduced?

(N/A) When a $dc$ source is connected to a capacitor, the capacitor gets charged and after charging, no current flows in the circuit; therefore, the lamp will not glow. There will be no change even if $C$ is reduced.
With an $ac$ source, the capacitor offers capacitive reactance $X_C = 1 / (\omega C)$ and current flows in the circuit. Consequently, the lamp will shine.
If the capacitance $C$ is reduced, the capacitive reactance $X_C = 1 / (\omega C)$ increases. As a result, the current in the circuit decreases, and the lamp will shine less brightly than before.