Question

A capacitor of capacitance C is being charged by connecting it across a DC source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor.

Answer 1

Hint: We shall first see all the phenomenon, while charging a capacitor, that is, is there any flow of current even for the slightest of moments. If so, then the ammeter will show a momentary deflection in its reading. But, in case if no current is produced even for the slightest of time during the charging of a capacitor, then no deflection will be shown by the ammeter in its reading.

Complete answer:
Let us assume that the capacitor is being charged by a DC voltage source. Then, we can say that, in the process of charging the capacitor, the charge on its plates keeps changing with time.
Let the charge on the capacitor at any time (t) be given by ‘q’.
The, the potential difference between the capacitors at any instant will be equal to:
$\Rightarrow V=\dfrac{q}{C}$
Where, C is the capacitance of the capacitor.
Since the charge on the capacitor will keep on changing till it has reached its steady state, the potential difference across the plate will also keep on changing. This time varying potential difference will produce a time varying electric field.
Let the electric field be E and the flux of this electric field through the capacitor plates be $\phi $ .
This time varying flux produces a current inside the plate of capacitors. This current is known as Displacement current and it is given by:
$\Rightarrow {{I}_{D}}={{\varepsilon }_{0}}\dfrac{d{{\phi }_{E}}}{dt}$
Thus, the ammeter will show a momentary deflection due to this Displacement current.
Also, the expression of current inside the capacitor is ${{\varepsilon }_{0}}\dfrac{d{{\phi }_{E}}}{dt}$.
The resulting continuity of current in the circuit is due to the constant electric field and constant charge on the plate of the capacitors achieved after getting in its steady state.

Note:
The generation of displacement current was added by Maxwell in his papers on further continuation of research on Ampere’s law. This addition basically removed an error from Ampere’s law. It is seen as one of the most important corrections in history and it has been one of the first basis of explaining the existence of electromagnetic waves.