Question

Q. 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 if the capacitance of the capacitor is reduced ?

Answer 1

With DC source, the lamp will glow for a moment and remain off. This is so because a fully discharged capacitor behaves like a short circuit, charges up and is an open circuit then on. Decreasing the capacitor has virtually no change in the behavior.
Capacitive reactance (x c)=1/(cw)=1/(c*2 πf)
As w=0 for DC capacitive reactance X will infinity and no current will flow in the circuit so the lamp will not glow even if we change the capacitance.

In case of AC source, the the lamp will remain lit at less than its normal brightness depending upon the impedance the capacitor offers. Decreasing the capacitance will further diminish the brightness of the lamp.
As Xc will be finite in the AC connection current will flow through the lamp.s o the lamp will glow . when we reduce C ,Xc increases and lamp will glow less bright