Seawater at a frequency f = 9 × 10 2   Hz , has permittivity ε = 80 ε 0 and resistivity…

Seawater at a frequency f=9×102 Hz, has permittivity ε=80ε0 and resistivity ρ=0.25 Ω m. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V(t)=V0sin(2πft). Then the conduction current density becomes 10x times the displacement current density after time t=1800 s. The value of x is _______

(Given :14πε0=9×109 N m2 C-2

Solution

Jc=Eρ=Vρd

Jd=1 Adqdt=CAdVcdt=ϵddVcdt

V0sin2πftρd=10x×80ε0 d V0(2πf)cos2πft

tan2π×900800=10x×409×109×900

=x=6

Asked in: JEE Main 2021 (17 Mar Shift 2)

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