bhu,
A capacitor is different to an inductor and your question seems not to recognise the differences between these devices.
A capacitor is a charge storage device. The charge in the capacitor (in the dielectric), and the voltage between the plates is given by the relationship; Q=C*V. Since the movement of charge is 'current', then Q = I*t.
When one changes the voltage across a capacitor, we are changing the charge. If we consider the rate of change of charge, there is a corresponding rate of change of voltage, which is related by the capacitance value. So for a step voltage change in the terminal voltage across a capacitor, there is a very high rate of change of voltage and consequently a high rate of change of charge. This high rate of change of charge, leads to a very large current flow.
With an inductor, the defining relationship is that; E = - L *di/dt. This is mathematically saying that the self induced voltage in an inductor is proportional to the rate of change of current in the inductor.
It is possible to force a sudden interruption to the flow of current in an inductor. In this case, the factor di/dt is very high and so the back emf across the inductor is also very high. However, when an inductor is connected across a voltage supply, the current will increase linearly with time and the rate of change of that current will be proportional to E/L.
So it is possible to have a high rate of change of terminal voltage with a capacitor and this requires a high current to either charge or discharge the capacitor.
Similarly, it is possible to have a high rate of change of current in an inductor, and this requires a high terminal voltage. Both of these situations require a supply with infinite current or voltage capacity, so often in the real world we dont see things exactly as they are supposed to be.
So your question was a bit not quite right, but you obviously have something in your mind. So maybe tell us what you had in your mind when you asked the question.
Hope this helps.