Question

The charging current for a capacitor is. 0.25A. What is the displacement current across its plates?

Answer 1

Hint
We know that in a circuit consisting of a capacitor and resistor the total current (i) is sum of charging current $({i_c})$ and displacement current $({i_d})$ i.e., $i = {i_c} + {i_d}$ . The displacement current is current through the capacitor. So, we will find out the charging current through the capacitor and find the displacement current by subtracting the charging current from total current i.e., $i - {i_c} = {i_d}$ …(i) .

Complete step by step answer
Inside the capacitor there is a gap between the plates of the capacitor and the current that passes through the capacitor is called displacement current. The charging current inside a capacitor is zero because initially the charge is zero on the capacitor and hence the potential is zero across the capacitor. But gradually the charge on the capacitor increases and when the capacitor is fully charged the whole potential falls across the capacitor and the voltage across the resistor is zero. So, the charging current is zero inside a capacitor. So, from equation (i)
 ${i_d} = i - {i_c}$
 $
   \Rightarrow {i_d} = i - 0 \\
   \Rightarrow {i_d} = i \\
   \Rightarrow {i_d} = 0.25A \\
 $
Therefore, the displacement current is .25A

Note
The displacement current across capacitor plates when capacitor is not charged is zero and it equals the total current when the capacitor is fully charged. So, ${i_d} \leqslant i$ .
The displacement current is given by,
 ${i_d} = {\varepsilon _o}\dfrac{{d{\phi _E}}}{{dt}}$
Where ${\phi _E}$ is the electric flux, ${\varepsilon _o}$ is permittivity of free space.