In the process of charging of a capacitor of capacitance C, the current produced between the plates of the capacitor is
(V and E are voltage and electric field across the capacitor, respectively)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( C\displaystyle\frac{dV}{dt} \)
No charge crosses the gap between the plates. The current there is the displacement current, produced by the changing electric flux, and it equals the conduction current in the connecting wires, so the current is continuous.
\( \displaystyle i_d = \varepsilon_0\frac{d\Phi_E}{dt} = \varepsilon_0 A\frac{dE}{dt} \)
For plates of area A a distance d apart, E = V/d and \( C = \varepsilon_0 A/d \):
\( \displaystyle i_d = \frac{\varepsilon_0 A}{d}\frac{dV}{dt} \)
\( \displaystyle i_d = C\frac{dV}{dt} \)
This is the same as the charging current \( dq/dt \), since q = CV.