During charging of capacitor, `I_C`. is the conduction current flowing in the wires connecting capacitor to the battery and `I_d` is the Displacement current flowing between the plates of the capacitor.

Options

A. `I_c gt I_d`
B. `I_c lt I_d `
C. `I_c = I_d`
D. No relation exists between `i_c ` and `I_d`

Answer

C

Explanation

According to continuity of current conduction current has to be equal to the displacement current hence `i_C =I_D`. We can prove it easily.
Let o be the instantaneous charge acquired by the plates of the capacitor at some instant of time. Electric field between the plates of the capacitor can be written as follows:
`E=(q )/(epsi_0 A)`
Electric flux associated with a plane parallel to plates of the capacitor having same area as that of plate of capacitor can be written as follows:
`phi = EA =(q )/(epsi_0)`
Displacement current can be written as follows:
` I_d =epsi_0 ( d phi) /(d t) = ( dq) /( dt) =i_c`
Hence displacement current between the plates of the capacitor is same as conduction current flowing in the wires.