JEE Main202117 Mar 2021Evening ShiftPhysicsCurrent ElectricityActual
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 and is driven by an alternating voltage source V ( t ) = V 0 sin ( 2 π f t ) . Then the conduction current density becomes 10 x times the displacement current density after time t = 1 800 s . The value of x is _______ (Given : 1
Correct answer
0
Step-by-step solution
J c = E ρ = V ρ d J d = 1   A d q d t = C A d V c d t = ϵ d d V c d t ⇒ V 0 sin 2 π ft ρ d = 10 x × 80 ε 0   d   V 0 ( 2 π f ) cos 2 π ft tan 2 π × 900 800 = 10 x × 40 9 × 10 9 × 900 = x = 6