a lamp is connected in series with capacitor.predict your observations for ac and dc connections.what happens when capacitance is decreased.?

In the AC connections,

 

Initially the lamp will shine when the capasitor is being charged. Once the capasitor is charged fully, it does not allow the current to pass through. Hence the circuit becomes open circuit and lamp do not shine.

 

In DC connections,

 

Depending on the frequency of applied voltage capasitor is continously being charged and discharged. Hence the current is continously flowing from the circuit causes the lamp shine.

 

In AC connections current is given by,

 

 

If the capasitance is decreased, 1/ωc factor in the denominator increases and hence the current decreases. Therefore brightness of the lamp decreases.