When a capacitor is connected to a battery, the current starts flowing in a circuit that charges the capacitor until the voltage between plates becomes equal to the voltage of the battery. Since between plates of a capacitor, there is an insulator or dielectric, how is it possible that current flows in a circuit with a capacitor.
According to Ohm's law, the current is inversely proportional to resistance and an insulator by definition has a big resistance, so the capacitor behaves as an open circuit.
Hence,the current does not flow through a capacitor