Sea water at frequency `v=4 xx 10^(8)` Hz has permittivity `epsilon ~~ 80 epsilon_(0)` permeability `mu= mu_(0)` and resistivity `rho= 0.25`M. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source `V(t) =V_(0) " sin "(2pivt).` What fraction of the conduction current density is the displacement current density ?

Options

A. `2//3`
B. `4//9`
C. `9//4`
D. `2`

Answer

C

Explanation

`V(t)=V_(0) sin 2pi upsilont`
Let distance between the plates = d.
Electric field `=(V(t))/(d)=(V_(0))/(d)sin 2piupsilont`
Conduction current density
`J_(c)=(E)/(rho)=(V_(0))/(rhod)sin 2pi upsilont=J_(o_(c)) sin 2pi upsilont`
where `J_(o_(c))` is maximum conduction currect density.
Displacement current density,
`J_(d)=epsilon(d)/(dt)[(V_(0))/(d)sin(2piupsilont)]=(2piupsilonepsilon)/(d)V_(0)cos 2piupsilont`
`J_(d)=j_(o_(d))cos(2piupsilont)`
`(J_(o_(d)))/(J_(o_(c)))=(2piupsilon)/(d)epsilon(V_(0))/(d)=2piupsilonepsilonrho=2pi(4xx10^(8))(80epsilon_(0))(0.25)`
`=(J_(o_(c)))/(J_(o_(d)))=(9xx10^(9))/(4xx10^(9))=(9)/(4)" "((1)/(4piepsilon_(0))=9xx10^(9)"N m"^(2)//C^(2))`