Question: Q. 12. A capacitor of capacitance ’ $C$ ’ is being charged by connecting it across a $d c$ 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.
U] [O.D. I, II, III 2012]
Show Answer
Solution:
Ans. Yes, the ammeter will show a momentary deflection.
The momentary deflection is due to the flow of electrons in the circuit during the charging process. During this process, the electric field between the capacitor plates is changing and hence a displacement current flows in the gap. Hence we can say that there is a continuity of current in the circuit.
Expression :
$$ I_{D}=\varepsilon_{0} \frac{d \phi_{E}}{d t} $$
[CBSE Marking Scheme 2013, 2012]
[AI Q. 13. When an ideal capacitor is charged by a $d c$ battery, no current flows. However when an $a c$ source is used, the current flows continuously. How does one explain this, based on the concept of displacement current? U [Delhi I, II, III 2012]
Ans. When an ideal capacitor is charged by a $d c$ battery, the charge flows (momentarily) till the capacitor gets fully charged. When an ac source is connected, then conduction current $i_{c}=\frac{d q}{d t}$ keeps on flowing in the connecting wires.
$1 / 2$
Due to the changing current, the charge deposited on the plates of the capacitor changes with time. This causes change in electric field between the plates of the capacitor which causes the electric flux to change and gives rise to a displacement current in the region between the plates of the capacitor. Displacement current is given by $I_{D}$
$$ I_{D}=\varepsilon_{0} \frac{d \phi_{\mathrm{E}}}{d t} $$
and is equal to the conduction current at all instants.
[CBSE Marking Scheme 2012]
