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Consider the situation of the previous problem. Define displacement resistance R^d = V/i^d of the space between the plates where V is the potential difference between the plates and i^d is the displacement current. Show that R^d varies with time as R^d = R(e^1/τ – 1).

Consider the situation of the previous problem. Define displacement resistance R^d = V/i^d of the space between the plates where V is the potential difference between the plates and i^d is the displacement current. Show that R^d varies with time as
R^d = R(e^1/τ – 1).

Grade:11

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Sol. E = Q/ϵ base 0 A (Electric field) ∅ = E.A. = Q/ϵ base 0 A A/2 = Q/ϵ base 0 2 i base 0 = ϵ base 0 d∅ base E/dt = ϵ base 0 d/dt (Q/ϵ base 0 2) = 1/2 (dQ/dt) = 1/2 d/dt (ECe^-t/RC) = 1/2 EC – 1/RC e^-t/RC = -E/2R e^-td/RE base 0λ

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