Why the capacitors works on ac only?

Generally capacitor gives infinite resistance to dc components(i.e., block the dc components). it allows the ac components to pass through.

The reactance of capacitance is inversely proportional to frequency . For DC supply as frequency is zero ,the reactance of capacitance is infinity . so capacitance behave like a open circuit for DC supply.. So capacitance will work only for AC supply.

Reactance of capacitor X = 1/(2πfc)

Since f=0, for dc frequency is zero.
So, Reactance X will be infinity for dc.

means capacitor blocks dc and allows only ac to pass.