Seawater at a frequency f=9 × 10^2 Hz, has permittivity ε=80 ε_0 and resistivity ρ=0.25 Ω m. Imagine a parallel plate capacitor is immersed in…

Seawater at a frequency $\displaystyle f=9 \times 10^2 \mathrm{~Hz}$, has permittivity $\displaystyle \varepsilon=80 \varepsilon_0$ and resistivity $\displaystyle \rho=0.25 \Omega \mathrm{~m}$. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source $\displaystyle \mathrm{V}(\mathrm{t})=\mathrm{V}_0 \sin (2 \pi f \mathrm{t})$. Then the conduction current density becomes $\displaystyle 10^x$ times the displacement current density after time $\displaystyle \mathrm{t}=\frac{1}{800} \mathrm{~s}$. The value of $\displaystyle x$ is \_\_\_\_. (Given : $\displaystyle \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}$ )