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 ?

Explanation

When dc source ( for example, a battery ) is connected to a series combination of lamp and capacitor, current flows through the lamp till the capacitor get charged up. But after that no current flows through the lamp because capacitor offers infinite resistance to the flows of direct current and hence blocks dc.
Here, even when capacitance is reduced after the charging is over no current would flow through the capacitor ( of course, time for which transient current flows would decrease in this case ).
When ac source is connected to series combination of lamp and capacitor, current flows through the lamp continously because of continous charging and discharging of a capacitor (giving rise to continous flow of displacement current between the plates of a capacitor ). Hence, lamp glows continously. Here rms value of current passing through the lamp is,
`I_(rms) = = ( V_(rms))/(sqrt(R^(2)+ X_(C )^(2)))`
When capacitance C is reduced magnitude of capacitive reactance `X_(C ) = ( 1)/(omega_(C ))` increases an dso `I_(rms)` decreases and so lamp will emit less amount of light. i.e., it would become dim.