Sea-water at a frequency f = 9 × 10² Hz, has permittivity ε = 80ε₀ and resistivity ρ = 0.25Ωm. 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 become 10ˣ times the displacement current density after time t = 1/800 s. The value of x is ______. [Given: 1/(4πε₀) = 9 × 10⁹ Nm²C⁻²]
Sea-water at a frequency f = 9 × 10² Hz, has permittivity ε = 80ε₀ and resistivity ρ = 0.25Ωm. 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 become 10ˣ times the displacement current density after time t = 1/800 s. The value of x is ______. [Given: 1/(4πε₀) = 9 × 10⁹ Nm²C⁻²]
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1 Answer
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Conduction current density, J? = E/ρ = (V/d) / ρ = (V? sin (2πft) / (pd)
Displacement current density, J? = ε (dE/dt) = (ε/d) (dV/dt) = (2πfε/d) * V? cos (2πft)
The ratio of their magnitudes is:
J? / J? = tan (2πft) / (2πfε? ρ) = tan (2π * 900) / (2π * 9 * 10? * 80ε? * 0.25) = 10?
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