A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2 , the level of liquid is d 3 , initially. Suppose, the liquid level decreases at a constant speed v , the time constant as a function of time is

Question

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2 , the level of liquid is d 3 , initially. Suppose, the liquid level decreases at a constant speed v , the time constant as a function of time is, 6 ε 0 R 5 d + 3 v t, ( 15 d + 9 v t ) ε 0 R 2 d 3 - 3 d v t - g v 2 t 2, 6 ε 0 R 5 d - 3 v t, ( 15 d - 9 v t ) ε 0 R 2 d 3 + 3 d v t - 9 v 2 t 2

MARKS App · Accepted Answer

We have, the time constant, τ = R C ' … i Now, C ' = C 1 C 2 C 1 + C 2 = A ε 0 d - x K A ε 0 x A ε 0 d - x + K A ε 0 x ∴ C ' = K A ε 0 x + K ( d - x ) Putting the value of C ' in Equation. (i), we get τ = R K A ε 0 d 3 - v t + k d - d 3 + v t ∵ x = d 3 - v t Given, A = 1 and K = 2 ∴ τ = 3 × 2 ε 0 × R d - 3 v t + 6 d - 2 d + 6 v t = 6 R ε 0 5 d + 3 v t

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