Question

Why does current in a steady state not flow in a capacitor connected across a battery? However momentary current does flow during charging or discharging of the capacitor. Explain. 

Answer 1

In steady state condition, voltage across the capacitor nearly equals to the voltage of the charging source. Hence net voltage acting in the circuit is zero. Due to this there is no flow of charge (current) through the circuit and hence the capacitor.

Now we know for an uncharged capacitor the potential difference across the capacitor is zero. So when it is connected to a battery, the battery begins to charge it by withdrawing the free electrons from one plate connected with the positive terminal of the battery of the capacitance and deposit on the other plate of the capacitor. So, due to this flow of charge, there exist a momentary current while charging of the capacitor. Now when the capacitor is fully charged i.e. voltage across the capacitor nearly equals to the voltage of the charging source, the current in the circuit vanishes.
Now in case of discharging of a charged capacitor, the battery gets replaced by a wire of say resistance R. Hence the capacitor itself acts as a battery now and flow of charge exists in the circuit from negative plate to the positive plate of the battery. This leads to momentary current in the circuit. As soon as the all the positive charges on one plate gets neutralised by the negative charges on the other plate, the flow of charge stops and hence the current.