Question

If I am connect capacitor in power circuit, it continuously consume power or it consume only one time for charging.

Answer 1

well it is always charging

Answer 2

It will consume power to charge and then, once fully charged, it will not consume anymore power.
This is because, once charged, the plates of the capacitor will have the same potential difference as the battery.
Since there is no potential difference between the battery and the plates any longer, there can be no more current flow.
So, no more power is consumed.

Answer 3

The capacitor is never charged 100%

Answer 4

While that is true, that was not the question.

Answer 5

well a capacitor continuously consumes power ,
it is just that the amount of power consumed is rapidly decreasing

Answer 6

the capacitor is not 100% charged but the charging happens in a asymptotic fashion. Hence it will consume power for an infinite time but the rate of consumption will be the (1/e) relation